Learning Outcome

Achivement Indicators

2.1 & 2.2

Demonstrate an understanding of factoring polynomials of degree greater than 2 (limited to polynomials of degree ≤ 5 with integral coefficients).

a. Explain how long division of a polynomial expression by a binomial expression of the form x − a, a∈ I , is related to synthetic division.

b. Divide a polynomial expression by a binomial expression of the form x − a, a∈ I , using long division or synthetic division.

c. Explain the relationship between the linear factors of a polynomial expression and the zeros of the corresponding polynomial function.

d. Explain the relationship between the remainder when a polynomial expression is divided by x − a, a∈ I , and the value of the polynomial expression at x = a (remainder theorem).

e. Explain and apply the factor theorem to express a polynomial expression as a product of factors.

2.3

Graph and analyze polynomial functions (limited to polynomial functions of degree ≤ 5 ).

a. Identify the polynomial functions in a set of functions, and explain the reasoning.

b. Explain the role of the constant term and leading coefficient in the equation of a polynomial function with respect to the graph of the function.

c. Generalize rules for graphing polynomial functions of odd or even degree.

d. Explain the relationship between: the zeros of a polynomial function the roots of the corresponding polynomial equation the x-intercepts of the graph of the polynomial function.

e. Explain how the multiplicity of a zero of a polynomial function affects the graph.

f. Sketch, with or without technology, the graph of a polynomial function.

g. Solve a problem by modelling a given situation with a polynomial function and analyzing the graph of the function.

2.4

Demonstrate an understanding of operations on, and compositions of, functions.

a. Sketch the graph of a function that is the sum, difference, product or quotient of two functions, given their graphs.

b. Write the equation of a function that is the sum, difference, product or quotient of two or more functions, given their equations.

c. Determine the domain and range of a function that is the sum, difference, product or quotient of two functions.

d. Write a function h(x) as the sum, difference, product or quotient of two or more functions.

2.5

Demonstrate an understanding of operations on, and compositions of, functions.

a. Determine the value of the composition of functions when evaluated at a point, including:

.

b. Determine, given the equations of two functions f(x) and g(x), the equation of the composite function: and explain any restrictions

c. Sketch, given the equations of two functions f(x) and g(x), the graph of the composite function: d. Write a function h(x) as the composition of two or more functions.

e. Write a function h(x) by combining two or more functions through operations on, and compositions of, functions

2.6

Graph and analyze radical functions (limited to functions involving one radical).

a. Sketch the graph of the function , using a table of values, and state the domain and range.

b. Sketch the graph of the function by applying transformations to the graph of the function , and state the domain and range.

c. Sketch the graph of the function , given the graph of the function , and explain the strategies used.

c. Compare the domain and range of the function , to the domain and range of the function , and explain why the domains and ranges may differ.

d. Describe the relationship between the roots of a radical equation and the x-intercepts of the graph of the corresponding radical function.

e. Determine, graphically, an approximate solution of a radical equation.

2.7

Graph and analyze rational functions (limited to numerators and denominators that are monomials, binomials or trinomials).

a. Graph, with or without technology, a rational function.

b. Analyze the graphs of a set of rational functions to identify common characteristics.

c. Explain the behaviour of the graph of a rational function for values of the variable near a non-permissible value.

d. Determine if the graph of a rational function will have an asymptote or a hole for a nonpermissible value.

e. Match a set of rational functions to their graphs, and explain the reasoning.

f. Describe the relationship between the roots of a rational equation and the x-intercepts of the graph of the corresponding rational function.

g. Determine, graphically, an approximate solution of a rational equation.

Demonstrate an understanding of factoring polynomials of degree greater than 2 (limited to polynomials of degree ≤ 5 with integral coefficients).

a. Explain how long division of a polynomial expression by a binomial expression of the form x − a, a∈ I , is related to synthetic division.

b. Divide a polynomial expression by a binomial expression of the form x − a, a∈ I , using long division or synthetic division.

c. Explain the relationship between the linear factors of a polynomial expression and the zeros of the corresponding polynomial function.

d. Explain the relationship between the remainder when a polynomial expression is divided by x − a, a∈ I , and the value of the polynomial expression at x = a (remainder theorem).

e. Explain and apply the factor theorem to express a polynomial expression as a product of factors.

Graph and analyze polynomial functions (limited to polynomial functions of degree ≤ 5 ).

a. Identify the polynomial functions in a set of functions, and explain the reasoning.

b. Explain the role of the constant term and leading coefficient in the equation of a polynomial function with respect to the graph of the function.

c. Generalize rules for graphing polynomial functions of odd or even degree.

d. Explain the relationship between: the zeros of a polynomial function the roots of the corresponding polynomial equation the x-intercepts of the graph of the polynomial function.

e. Explain how the multiplicity of a zero of a polynomial function affects the graph.

f. Sketch, with or without technology, the graph of a polynomial function.

g. Solve a problem by modelling a given situation with a polynomial function and analyzing the graph of the function.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Sketch the graph of a function that is the sum, difference, product or quotient of two functions, given their graphs.

b. Write the equation of a function that is the sum, difference, product or quotient of two or more functions, given their equations.

c. Determine the domain and range of a function that is the sum, difference, product or quotient of two functions.

d. Write a function h(x) as the sum, difference, product or quotient of two or more functions.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Determine the value of the composition of functions when evaluated at a point, including:

.

b. Determine, given the equations of two functions f(x) and g(x), the equation of the composite function: and explain any restrictions

c. Sketch, given the equations of two functions f(x) and g(x), the graph of the composite function: d. Write a function h(x) as the composition of two or more functions.

e. Write a function h(x) by combining two or more functions through operations on, and compositions of, functions

Demonstrate an understanding of factoring polynomials of degree greater than 2 (limited to polynomials of degree ≤ 5 with integral coefficients).

a. Explain how long division of a polynomial expression by a binomial expression of the form x − a, a∈ I , is related to synthetic division.

b. Divide a polynomial expression by a binomial expression of the form x − a, a∈ I , using long division or synthetic division.

c. Explain the relationship between the linear factors of a polynomial expression and the zeros of the corresponding polynomial function.

d. Explain the relationship between the remainder when a polynomial expression is divided by x − a, a∈ I , and the value of the polynomial expression at x = a (remainder theorem).

e. Explain and apply the factor theorem to express a polynomial expression as a product of factors.

Graph and analyze polynomial functions (limited to polynomial functions of degree ≤ 5 ).

a. Identify the polynomial functions in a set of functions, and explain the reasoning.

b. Explain the role of the constant term and leading coefficient in the equation of a polynomial function with respect to the graph of the function.

c. Generalize rules for graphing polynomial functions of odd or even degree.

d. Explain the relationship between: the zeros of a polynomial function the roots of the corresponding polynomial equation the x-intercepts of the graph of the polynomial function.

e. Explain how the multiplicity of a zero of a polynomial function affects the graph.

f. Sketch, with or without technology, the graph of a polynomial function.

g. Solve a problem by modelling a given situation with a polynomial function and analyzing the graph of the function.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Sketch the graph of a function that is the sum, difference, product or quotient of two functions, given their graphs.

b. Write the equation of a function that is the sum, difference, product or quotient of two or more functions, given their equations.

c. Determine the domain and range of a function that is the sum, difference, product or quotient of two functions.

d. Write a function h(x) as the sum, difference, product or quotient of two or more functions.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Determine the value of the composition of functions when evaluated at a point, including:

.

b. Determine, given the equations of two functions f(x) and g(x), the equation of the composite function: and explain any restrictions

c. Sketch, given the equations of two functions f(x) and g(x), the graph of the composite function: d. Write a function h(x) as the composition of two or more functions.

e. Write a function h(x) by combining two or more functions through operations on, and compositions of, functions

Demonstrate an understanding of factoring polynomials of degree greater than 2 (limited to polynomials of degree ≤ 5 with integral coefficients).

a. Explain how long division of a polynomial expression by a binomial expression of the form x − a, a∈ I , is related to synthetic division.

b. Divide a polynomial expression by a binomial expression of the form x − a, a∈ I , using long division or synthetic division.

c. Explain the relationship between the linear factors of a polynomial expression and the zeros of the corresponding polynomial function.

d. Explain the relationship between the remainder when a polynomial expression is divided by x − a, a∈ I , and the value of the polynomial expression at x = a (remainder theorem).

e. Explain and apply the factor theorem to express a polynomial expression as a product of factors.

Graph and analyze polynomial functions (limited to polynomial functions of degree ≤ 5 ).

a. Identify the polynomial functions in a set of functions, and explain the reasoning.

b. Explain the role of the constant term and leading coefficient in the equation of a polynomial function with respect to the graph of the function.

c. Generalize rules for graphing polynomial functions of odd or even degree.

d. Explain the relationship between: the zeros of a polynomial function the roots of the corresponding polynomial equation the x-intercepts of the graph of the polynomial function.

e. Explain how the multiplicity of a zero of a polynomial function affects the graph.

f. Sketch, with or without technology, the graph of a polynomial function.

g. Solve a problem by modelling a given situation with a polynomial function and analyzing the graph of the function.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Sketch the graph of a function that is the sum, difference, product or quotient of two functions, given their graphs.

b. Write the equation of a function that is the sum, difference, product or quotient of two or more functions, given their equations.

c. Determine the domain and range of a function that is the sum, difference, product or quotient of two functions.

d. Write a function h(x) as the sum, difference, product or quotient of two or more functions.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Determine the value of the composition of functions when evaluated at a point, including:

.

b. Determine, given the equations of two functions f(x) and g(x), the equation of the composite function: and explain any restrictions

c. Sketch, given the equations of two functions f(x) and g(x), the graph of the composite function: d. Write a function h(x) as the composition of two or more functions.

e. Write a function h(x) by combining two or more functions through operations on, and compositions of, functions

Demonstrate an understanding of factoring polynomials of degree greater than 2 (limited to polynomials of degree ≤ 5 with integral coefficients).

a. Explain how long division of a polynomial expression by a binomial expression of the form x − a, a∈ I , is related to synthetic division.

b. Divide a polynomial expression by a binomial expression of the form x − a, a∈ I , using long division or synthetic division.

c. Explain the relationship between the linear factors of a polynomial expression and the zeros of the corresponding polynomial function.

d. Explain the relationship between the remainder when a polynomial expression is divided by x − a, a∈ I , and the value of the polynomial expression at x = a (remainder theorem).

e. Explain and apply the factor theorem to express a polynomial expression as a product of factors.

Graph and analyze polynomial functions (limited to polynomial functions of degree ≤ 5 ).

a. Identify the polynomial functions in a set of functions, and explain the reasoning.

b. Explain the role of the constant term and leading coefficient in the equation of a polynomial function with respect to the graph of the function.

c. Generalize rules for graphing polynomial functions of odd or even degree.

d. Explain the relationship between: the zeros of a polynomial function the roots of the corresponding polynomial equation the x-intercepts of the graph of the polynomial function.

e. Explain how the multiplicity of a zero of a polynomial function affects the graph.

f. Sketch, with or without technology, the graph of a polynomial function.

g. Solve a problem by modelling a given situation with a polynomial function and analyzing the graph of the function.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Sketch the graph of a function that is the sum, difference, product or quotient of two functions, given their graphs.

b. Write the equation of a function that is the sum, difference, product or quotient of two or more functions, given their equations.

c. Determine the domain and range of a function that is the sum, difference, product or quotient of two functions.

d. Write a function h(x) as the sum, difference, product or quotient of two or more functions.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Determine the value of the composition of functions when evaluated at a point, including:

.

b. Determine, given the equations of two functions f(x) and g(x), the equation of the composite function: and explain any restrictions

c. Sketch, given the equations of two functions f(x) and g(x), the graph of the composite function: d. Write a function h(x) as the composition of two or more functions.

e. Write a function h(x) by combining two or more functions through operations on, and compositions of, functions

Demonstrate an understanding of factoring polynomials of degree greater than 2 (limited to polynomials of degree ≤ 5 with integral coefficients).

a. Explain how long division of a polynomial expression by a binomial expression of the form x − a, a∈ I , is related to synthetic division.

b. Divide a polynomial expression by a binomial expression of the form x − a, a∈ I , using long division or synthetic division.

c. Explain the relationship between the linear factors of a polynomial expression and the zeros of the corresponding polynomial function.

d. Explain the relationship between the remainder when a polynomial expression is divided by x − a, a∈ I , and the value of the polynomial expression at x = a (remainder theorem).

e. Explain and apply the factor theorem to express a polynomial expression as a product of factors.

Graph and analyze polynomial functions (limited to polynomial functions of degree ≤ 5 ).

a. Identify the polynomial functions in a set of functions, and explain the reasoning.

b. Explain the role of the constant term and leading coefficient in the equation of a polynomial function with respect to the graph of the function.

c. Generalize rules for graphing polynomial functions of odd or even degree.

d. Explain the relationship between: the zeros of a polynomial function the roots of the corresponding polynomial equation the x-intercepts of the graph of the polynomial function.

e. Explain how the multiplicity of a zero of a polynomial function affects the graph.

f. Sketch, with or without technology, the graph of a polynomial function.

g. Solve a problem by modelling a given situation with a polynomial function and analyzing the graph of the function.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Sketch the graph of a function that is the sum, difference, product or quotient of two functions, given their graphs.

b. Write the equation of a function that is the sum, difference, product or quotient of two or more functions, given their equations.

c. Determine the domain and range of a function that is the sum, difference, product or quotient of two functions.

d. Write a function h(x) as the sum, difference, product or quotient of two or more functions.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Determine the value of the composition of functions when evaluated at a point, including:

.

b. Determine, given the equations of two functions f(x) and g(x), the equation of the composite function: and explain any restrictions

c. Sketch, given the equations of two functions f(x) and g(x), the graph of the composite function: d. Write a function h(x) as the composition of two or more functions.

e. Write a function h(x) by combining two or more functions through operations on, and compositions of, functions

Demonstrate an understanding of factoring polynomials of degree greater than 2 (limited to polynomials of degree ≤ 5 with integral coefficients).

a. Explain how long division of a polynomial expression by a binomial expression of the form x − a, a∈ I , is related to synthetic division.

b. Divide a polynomial expression by a binomial expression of the form x − a, a∈ I , using long division or synthetic division.

c. Explain the relationship between the linear factors of a polynomial expression and the zeros of the corresponding polynomial function.

d. Explain the relationship between the remainder when a polynomial expression is divided by x − a, a∈ I , and the value of the polynomial expression at x = a (remainder theorem).

e. Explain and apply the factor theorem to express a polynomial expression as a product of factors.

Graph and analyze polynomial functions (limited to polynomial functions of degree ≤ 5 ).

a. Identify the polynomial functions in a set of functions, and explain the reasoning.

b. Explain the role of the constant term and leading coefficient in the equation of a polynomial function with respect to the graph of the function.

c. Generalize rules for graphing polynomial functions of odd or even degree.

d. Explain the relationship between: the zeros of a polynomial function the roots of the corresponding polynomial equation the x-intercepts of the graph of the polynomial function.

e. Explain how the multiplicity of a zero of a polynomial function affects the graph.

f. Sketch, with or without technology, the graph of a polynomial function.

g. Solve a problem by modelling a given situation with a polynomial function and analyzing the graph of the function.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Sketch the graph of a function that is the sum, difference, product or quotient of two functions, given their graphs.

b. Write the equation of a function that is the sum, difference, product or quotient of two or more functions, given their equations.

c. Determine the domain and range of a function that is the sum, difference, product or quotient of two functions.

d. Write a function h(x) as the sum, difference, product or quotient of two or more functions.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Determine the value of the composition of functions when evaluated at a point, including:

.

b. Determine, given the equations of two functions f(x) and g(x), the equation of the composite function: and explain any restrictions

c. Sketch, given the equations of two functions f(x) and g(x), the graph of the composite function: d. Write a function h(x) as the composition of two or more functions.

e. Write a function h(x) by combining two or more functions through operations on, and compositions of, functions

Demonstrate an understanding of factoring polynomials of degree greater than 2 (limited to polynomials of degree ≤ 5 with integral coefficients).

a. Explain how long division of a polynomial expression by a binomial expression of the form x − a, a∈ I , is related to synthetic division.

b. Divide a polynomial expression by a binomial expression of the form x − a, a∈ I , using long division or synthetic division.

c. Explain the relationship between the linear factors of a polynomial expression and the zeros of the corresponding polynomial function.

d. Explain the relationship between the remainder when a polynomial expression is divided by x − a, a∈ I , and the value of the polynomial expression at x = a (remainder theorem).

e. Explain and apply the factor theorem to express a polynomial expression as a product of factors.

Graph and analyze polynomial functions (limited to polynomial functions of degree ≤ 5 ).

a. Identify the polynomial functions in a set of functions, and explain the reasoning.

b. Explain the role of the constant term and leading coefficient in the equation of a polynomial function with respect to the graph of the function.

c. Generalize rules for graphing polynomial functions of odd or even degree.

d. Explain the relationship between: the zeros of a polynomial function the roots of the corresponding polynomial equation the x-intercepts of the graph of the polynomial function.

e. Explain how the multiplicity of a zero of a polynomial function affects the graph.

f. Sketch, with or without technology, the graph of a polynomial function.

g. Solve a problem by modelling a given situation with a polynomial function and analyzing the graph of the function.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Sketch the graph of a function that is the sum, difference, product or quotient of two functions, given their graphs.

b. Write the equation of a function that is the sum, difference, product or quotient of two or more functions, given their equations.

c. Determine the domain and range of a function that is the sum, difference, product or quotient of two functions.

d. Write a function h(x) as the sum, difference, product or quotient of two or more functions.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Determine the value of the composition of functions when evaluated at a point, including:

.

b. Determine, given the equations of two functions f(x) and g(x), the equation of the composite function: and explain any restrictions

c. Sketch, given the equations of two functions f(x) and g(x), the graph of the composite function: d. Write a function h(x) as the composition of two or more functions.

e. Write a function h(x) by combining two or more functions through operations on, and compositions of, functions

Demonstrate an understanding of factoring polynomials of degree greater than 2 (limited to polynomials of degree ≤ 5 with integral coefficients).

a. Explain how long division of a polynomial expression by a binomial expression of the form x − a, a∈ I , is related to synthetic division.

b. Divide a polynomial expression by a binomial expression of the form x − a, a∈ I , using long division or synthetic division.

c. Explain the relationship between the linear factors of a polynomial expression and the zeros of the corresponding polynomial function.

d. Explain the relationship between the remainder when a polynomial expression is divided by x − a, a∈ I , and the value of the polynomial expression at x = a (remainder theorem).

e. Explain and apply the factor theorem to express a polynomial expression as a product of factors.

Graph and analyze polynomial functions (limited to polynomial functions of degree ≤ 5 ).

a. Identify the polynomial functions in a set of functions, and explain the reasoning.

b. Explain the role of the constant term and leading coefficient in the equation of a polynomial function with respect to the graph of the function.

c. Generalize rules for graphing polynomial functions of odd or even degree.

d. Explain the relationship between: the zeros of a polynomial function the roots of the corresponding polynomial equation the x-intercepts of the graph of the polynomial function.

e. Explain how the multiplicity of a zero of a polynomial function affects the graph.

f. Sketch, with or without technology, the graph of a polynomial function.

g. Solve a problem by modelling a given situation with a polynomial function and analyzing the graph of the function.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Sketch the graph of a function that is the sum, difference, product or quotient of two functions, given their graphs.

b. Write the equation of a function that is the sum, difference, product or quotient of two or more functions, given their equations.

c. Determine the domain and range of a function that is the sum, difference, product or quotient of two functions.

d. Write a function h(x) as the sum, difference, product or quotient of two or more functions.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Determine the value of the composition of functions when evaluated at a point, including:

.

b. Determine, given the equations of two functions f(x) and g(x), the equation of the composite function: and explain any restrictions

c. Sketch, given the equations of two functions f(x) and g(x), the graph of the composite function: d. Write a function h(x) as the composition of two or more functions.

e. Write a function h(x) by combining two or more functions through operations on, and compositions of, functions

Demonstrate an understanding of factoring polynomials of degree greater than 2 (limited to polynomials of degree ≤ 5 with integral coefficients).

a. Explain how long division of a polynomial expression by a binomial expression of the form x − a, a∈ I , is related to synthetic division.

b. Divide a polynomial expression by a binomial expression of the form x − a, a∈ I , using long division or synthetic division.

c. Explain the relationship between the linear factors of a polynomial expression and the zeros of the corresponding polynomial function.

d. Explain the relationship between the remainder when a polynomial expression is divided by x − a, a∈ I , and the value of the polynomial expression at x = a (remainder theorem).

e. Explain and apply the factor theorem to express a polynomial expression as a product of factors.

Graph and analyze polynomial functions (limited to polynomial functions of degree ≤ 5 ).

a. Identify the polynomial functions in a set of functions, and explain the reasoning.

b. Explain the role of the constant term and leading coefficient in the equation of a polynomial function with respect to the graph of the function.

c. Generalize rules for graphing polynomial functions of odd or even degree.

d. Explain the relationship between: the zeros of a polynomial function the roots of the corresponding polynomial equation the x-intercepts of the graph of the polynomial function.

e. Explain how the multiplicity of a zero of a polynomial function affects the graph.

f. Sketch, with or without technology, the graph of a polynomial function.

g. Solve a problem by modelling a given situation with a polynomial function and analyzing the graph of the function.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Sketch the graph of a function that is the sum, difference, product or quotient of two functions, given their graphs.

b. Write the equation of a function that is the sum, difference, product or quotient of two or more functions, given their equations.

c. Determine the domain and range of a function that is the sum, difference, product or quotient of two functions.

d. Write a function h(x) as the sum, difference, product or quotient of two or more functions.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Determine the value of the composition of functions when evaluated at a point, including:

.

b. Determine, given the equations of two functions f(x) and g(x), the equation of the composite function: and explain any restrictions

c. Sketch, given the equations of two functions f(x) and g(x), the graph of the composite function: d. Write a function h(x) as the composition of two or more functions.

e. Write a function h(x) by combining two or more functions through operations on, and compositions of, functions

Demonstrate an understanding of factoring polynomials of degree greater than 2 (limited to polynomials of degree ≤ 5 with integral coefficients).

a. Explain how long division of a polynomial expression by a binomial expression of the form x − a, a∈ I , is related to synthetic division.

b. Divide a polynomial expression by a binomial expression of the form x − a, a∈ I , using long division or synthetic division.

c. Explain the relationship between the linear factors of a polynomial expression and the zeros of the corresponding polynomial function.

d. Explain the relationship between the remainder when a polynomial expression is divided by x − a, a∈ I , and the value of the polynomial expression at x = a (remainder theorem).

e. Explain and apply the factor theorem to express a polynomial expression as a product of factors.

Graph and analyze polynomial functions (limited to polynomial functions of degree ≤ 5 ).

a. Identify the polynomial functions in a set of functions, and explain the reasoning.

b. Explain the role of the constant term and leading coefficient in the equation of a polynomial function with respect to the graph of the function.

c. Generalize rules for graphing polynomial functions of odd or even degree.

d. Explain the relationship between: the zeros of a polynomial function the roots of the corresponding polynomial equation the x-intercepts of the graph of the polynomial function.

e. Explain how the multiplicity of a zero of a polynomial function affects the graph.

f. Sketch, with or without technology, the graph of a polynomial function.

g. Solve a problem by modelling a given situation with a polynomial function and analyzing the graph of the function.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Sketch the graph of a function that is the sum, difference, product or quotient of two functions, given their graphs.

b. Write the equation of a function that is the sum, difference, product or quotient of two or more functions, given their equations.

c. Determine the domain and range of a function that is the sum, difference, product or quotient of two functions.

d. Write a function h(x) as the sum, difference, product or quotient of two or more functions.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Determine the value of the composition of functions when evaluated at a point, including:

.

b. Determine, given the equations of two functions f(x) and g(x), the equation of the composite function: and explain any restrictions

c. Sketch, given the equations of two functions f(x) and g(x), the graph of the composite function: d. Write a function h(x) as the composition of two or more functions.

e. Write a function h(x) by combining two or more functions through operations on, and compositions of, functions

Demonstrate an understanding of factoring polynomials of degree greater than 2 (limited to polynomials of degree ≤ 5 with integral coefficients).

a. Explain how long division of a polynomial expression by a binomial expression of the form x − a, a∈ I , is related to synthetic division.

b. Divide a polynomial expression by a binomial expression of the form x − a, a∈ I , using long division or synthetic division.

c. Explain the relationship between the linear factors of a polynomial expression and the zeros of the corresponding polynomial function.

d. Explain the relationship between the remainder when a polynomial expression is divided by x − a, a∈ I , and the value of the polynomial expression at x = a (remainder theorem).

e. Explain and apply the factor theorem to express a polynomial expression as a product of factors.

Graph and analyze polynomial functions (limited to polynomial functions of degree ≤ 5 ).

a. Identify the polynomial functions in a set of functions, and explain the reasoning.

b. Explain the role of the constant term and leading coefficient in the equation of a polynomial function with respect to the graph of the function.

c. Generalize rules for graphing polynomial functions of odd or even degree.

d. Explain the relationship between: the zeros of a polynomial function the roots of the corresponding polynomial equation the x-intercepts of the graph of the polynomial function.

e. Explain how the multiplicity of a zero of a polynomial function affects the graph.

f. Sketch, with or without technology, the graph of a polynomial function.

g. Solve a problem by modelling a given situation with a polynomial function and analyzing the graph of the function.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Sketch the graph of a function that is the sum, difference, product or quotient of two functions, given their graphs.

b. Write the equation of a function that is the sum, difference, product or quotient of two or more functions, given their equations.

c. Determine the domain and range of a function that is the sum, difference, product or quotient of two functions.

d. Write a function h(x) as the sum, difference, product or quotient of two or more functions.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Determine the value of the composition of functions when evaluated at a point, including:

.

b. Determine, given the equations of two functions f(x) and g(x), the equation of the composite function: and explain any restrictions

c. Sketch, given the equations of two functions f(x) and g(x), the graph of the composite function: d. Write a function h(x) as the composition of two or more functions.

e. Write a function h(x) by combining two or more functions through operations on, and compositions of, functions

Demonstrate an understanding of factoring polynomials of degree greater than 2 (limited to polynomials of degree ≤ 5 with integral coefficients).

a. Explain how long division of a polynomial expression by a binomial expression of the form x − a, a∈ I , is related to synthetic division.

b. Divide a polynomial expression by a binomial expression of the form x − a, a∈ I , using long division or synthetic division.

c. Explain the relationship between the linear factors of a polynomial expression and the zeros of the corresponding polynomial function.

d. Explain the relationship between the remainder when a polynomial expression is divided by x − a, a∈ I , and the value of the polynomial expression at x = a (remainder theorem).

e. Explain and apply the factor theorem to express a polynomial expression as a product of factors.

Graph and analyze polynomial functions (limited to polynomial functions of degree ≤ 5 ).

a. Identify the polynomial functions in a set of functions, and explain the reasoning.

b. Explain the role of the constant term and leading coefficient in the equation of a polynomial function with respect to the graph of the function.

c. Generalize rules for graphing polynomial functions of odd or even degree.

d. Explain the relationship between: the zeros of a polynomial function the roots of the corresponding polynomial equation the x-intercepts of the graph of the polynomial function.

e. Explain how the multiplicity of a zero of a polynomial function affects the graph.

f. Sketch, with or without technology, the graph of a polynomial function.

g. Solve a problem by modelling a given situation with a polynomial function and analyzing the graph of the function.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Sketch the graph of a function that is the sum, difference, product or quotient of two functions, given their graphs.

b. Write the equation of a function that is the sum, difference, product or quotient of two or more functions, given their equations.

c. Determine the domain and range of a function that is the sum, difference, product or quotient of two functions.

d. Write a function h(x) as the sum, difference, product or quotient of two or more functions.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Determine the value of the composition of functions when evaluated at a point, including:

.

b. Determine, given the equations of two functions f(x) and g(x), the equation of the composite function: and explain any restrictions

c. Sketch, given the equations of two functions f(x) and g(x), the graph of the composite function: d. Write a function h(x) as the composition of two or more functions.

e. Write a function h(x) by combining two or more functions through operations on, and compositions of, functions

Demonstrate an understanding of factoring polynomials of degree greater than 2 (limited to polynomials of degree ≤ 5 with integral coefficients).

a. Explain how long division of a polynomial expression by a binomial expression of the form x − a, a∈ I , is related to synthetic division.

b. Divide a polynomial expression by a binomial expression of the form x − a, a∈ I , using long division or synthetic division.

c. Explain the relationship between the linear factors of a polynomial expression and the zeros of the corresponding polynomial function.

d. Explain the relationship between the remainder when a polynomial expression is divided by x − a, a∈ I , and the value of the polynomial expression at x = a (remainder theorem).

e. Explain and apply the factor theorem to express a polynomial expression as a product of factors.

Graph and analyze polynomial functions (limited to polynomial functions of degree ≤ 5 ).

a. Identify the polynomial functions in a set of functions, and explain the reasoning.

b. Explain the role of the constant term and leading coefficient in the equation of a polynomial function with respect to the graph of the function.

c. Generalize rules for graphing polynomial functions of odd or even degree.

d. Explain the relationship between: the zeros of a polynomial function the roots of the corresponding polynomial equation the x-intercepts of the graph of the polynomial function.

e. Explain how the multiplicity of a zero of a polynomial function affects the graph.

f. Sketch, with or without technology, the graph of a polynomial function.

g. Solve a problem by modelling a given situation with a polynomial function and analyzing the graph of the function.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Sketch the graph of a function that is the sum, difference, product or quotient of two functions, given their graphs.

b. Write the equation of a function that is the sum, difference, product or quotient of two or more functions, given their equations.

c. Determine the domain and range of a function that is the sum, difference, product or quotient of two functions.

d. Write a function h(x) as the sum, difference, product or quotient of two or more functions.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Determine the value of the composition of functions when evaluated at a point, including:

.

b. Determine, given the equations of two functions f(x) and g(x), the equation of the composite function: and explain any restrictions

c. Sketch, given the equations of two functions f(x) and g(x), the graph of the composite function: d. Write a function h(x) as the composition of two or more functions.

e. Write a function h(x) by combining two or more functions through operations on, and compositions of, functions

Demonstrate an understanding of factoring polynomials of degree greater than 2 (limited to polynomials of degree ≤ 5 with integral coefficients).

a. Explain how long division of a polynomial expression by a binomial expression of the form x − a, a∈ I , is related to synthetic division.

b. Divide a polynomial expression by a binomial expression of the form x − a, a∈ I , using long division or synthetic division.

c. Explain the relationship between the linear factors of a polynomial expression and the zeros of the corresponding polynomial function.

d. Explain the relationship between the remainder when a polynomial expression is divided by x − a, a∈ I , and the value of the polynomial expression at x = a (remainder theorem).

e. Explain and apply the factor theorem to express a polynomial expression as a product of factors.

Graph and analyze polynomial functions (limited to polynomial functions of degree ≤ 5 ).

a. Identify the polynomial functions in a set of functions, and explain the reasoning.

b. Explain the role of the constant term and leading coefficient in the equation of a polynomial function with respect to the graph of the function.

c. Generalize rules for graphing polynomial functions of odd or even degree.

d. Explain the relationship between: the zeros of a polynomial function the roots of the corresponding polynomial equation the x-intercepts of the graph of the polynomial function.

e. Explain how the multiplicity of a zero of a polynomial function affects the graph.

f. Sketch, with or without technology, the graph of a polynomial function.

g. Solve a problem by modelling a given situation with a polynomial function and analyzing the graph of the function.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Sketch the graph of a function that is the sum, difference, product or quotient of two functions, given their graphs.

b. Write the equation of a function that is the sum, difference, product or quotient of two or more functions, given their equations.

c. Determine the domain and range of a function that is the sum, difference, product or quotient of two functions.

d. Write a function h(x) as the sum, difference, product or quotient of two or more functions.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Determine the value of the composition of functions when evaluated at a point, including:

.

b. Determine, given the equations of two functions f(x) and g(x), the equation of the composite function: and explain any restrictions

c. Sketch, given the equations of two functions f(x) and g(x), the graph of the composite function: d. Write a function h(x) as the composition of two or more functions.

e. Write a function h(x) by combining two or more functions through operations on, and compositions of, functions

Demonstrate an understanding of factoring polynomials of degree greater than 2 (limited to polynomials of degree ≤ 5 with integral coefficients).

a. Explain how long division of a polynomial expression by a binomial expression of the form x − a, a∈ I , is related to synthetic division.

b. Divide a polynomial expression by a binomial expression of the form x − a, a∈ I , using long division or synthetic division.

c. Explain the relationship between the linear factors of a polynomial expression and the zeros of the corresponding polynomial function.

d. Explain the relationship between the remainder when a polynomial expression is divided by x − a, a∈ I , and the value of the polynomial expression at x = a (remainder theorem).

e. Explain and apply the factor theorem to express a polynomial expression as a product of factors.

Graph and analyze polynomial functions (limited to polynomial functions of degree ≤ 5 ).

a. Identify the polynomial functions in a set of functions, and explain the reasoning.

b. Explain the role of the constant term and leading coefficient in the equation of a polynomial function with respect to the graph of the function.

c. Generalize rules for graphing polynomial functions of odd or even degree.

d. Explain the relationship between: the zeros of a polynomial function the roots of the corresponding polynomial equation the x-intercepts of the graph of the polynomial function.

e. Explain how the multiplicity of a zero of a polynomial function affects the graph.

f. Sketch, with or without technology, the graph of a polynomial function.

g. Solve a problem by modelling a given situation with a polynomial function and analyzing the graph of the function.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Sketch the graph of a function that is the sum, difference, product or quotient of two functions, given their graphs.

b. Write the equation of a function that is the sum, difference, product or quotient of two or more functions, given their equations.

c. Determine the domain and range of a function that is the sum, difference, product or quotient of two functions.

d. Write a function h(x) as the sum, difference, product or quotient of two or more functions.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Determine the value of the composition of functions when evaluated at a point, including:

.

b. Determine, given the equations of two functions f(x) and g(x), the equation of the composite function: and explain any restrictions

c. Sketch, given the equations of two functions f(x) and g(x), the graph of the composite function: d. Write a function h(x) as the composition of two or more functions.

e. Write a function h(x) by combining two or more functions through operations on, and compositions of, functions

Demonstrate an understanding of factoring polynomials of degree greater than 2 (limited to polynomials of degree ≤ 5 with integral coefficients).

a. Explain how long division of a polynomial expression by a binomial expression of the form x − a, a∈ I , is related to synthetic division.

b. Divide a polynomial expression by a binomial expression of the form x − a, a∈ I , using long division or synthetic division.

c. Explain the relationship between the linear factors of a polynomial expression and the zeros of the corresponding polynomial function.

d. Explain the relationship between the remainder when a polynomial expression is divided by x − a, a∈ I , and the value of the polynomial expression at x = a (remainder theorem).

e. Explain and apply the factor theorem to express a polynomial expression as a product of factors.

Graph and analyze polynomial functions (limited to polynomial functions of degree ≤ 5 ).

a. Identify the polynomial functions in a set of functions, and explain the reasoning.

b. Explain the role of the constant term and leading coefficient in the equation of a polynomial function with respect to the graph of the function.

c. Generalize rules for graphing polynomial functions of odd or even degree.

d. Explain the relationship between: the zeros of a polynomial function the roots of the corresponding polynomial equation the x-intercepts of the graph of the polynomial function.

e. Explain how the multiplicity of a zero of a polynomial function affects the graph.

f. Sketch, with or without technology, the graph of a polynomial function.

g. Solve a problem by modelling a given situation with a polynomial function and analyzing the graph of the function.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Sketch the graph of a function that is the sum, difference, product or quotient of two functions, given their graphs.

b. Write the equation of a function that is the sum, difference, product or quotient of two or more functions, given their equations.

c. Determine the domain and range of a function that is the sum, difference, product or quotient of two functions.

d. Write a function h(x) as the sum, difference, product or quotient of two or more functions.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Determine the value of the composition of functions when evaluated at a point, including:

.

b. Determine, given the equations of two functions f(x) and g(x), the equation of the composite function: and explain any restrictions

c. Sketch, given the equations of two functions f(x) and g(x), the graph of the composite function: d. Write a function h(x) as the composition of two or more functions.

e. Write a function h(x) by combining two or more functions through operations on, and compositions of, functions

Demonstrate an understanding of factoring polynomials of degree greater than 2 (limited to polynomials of degree ≤ 5 with integral coefficients).

a. Explain how long division of a polynomial expression by a binomial expression of the form x − a, a∈ I , is related to synthetic division.

b. Divide a polynomial expression by a binomial expression of the form x − a, a∈ I , using long division or synthetic division.

c. Explain the relationship between the linear factors of a polynomial expression and the zeros of the corresponding polynomial function.

d. Explain the relationship between the remainder when a polynomial expression is divided by x − a, a∈ I , and the value of the polynomial expression at x = a (remainder theorem).

e. Explain and apply the factor theorem to express a polynomial expression as a product of factors.

Graph and analyze polynomial functions (limited to polynomial functions of degree ≤ 5 ).

a. Identify the polynomial functions in a set of functions, and explain the reasoning.

b. Explain the role of the constant term and leading coefficient in the equation of a polynomial function with respect to the graph of the function.

c. Generalize rules for graphing polynomial functions of odd or even degree.

d. Explain the relationship between: the zeros of a polynomial function the roots of the corresponding polynomial equation the x-intercepts of the graph of the polynomial function.

e. Explain how the multiplicity of a zero of a polynomial function affects the graph.

f. Sketch, with or without technology, the graph of a polynomial function.

g. Solve a problem by modelling a given situation with a polynomial function and analyzing the graph of the function.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Sketch the graph of a function that is the sum, difference, product or quotient of two functions, given their graphs.

b. Write the equation of a function that is the sum, difference, product or quotient of two or more functions, given their equations.

c. Determine the domain and range of a function that is the sum, difference, product or quotient of two functions.

d. Write a function h(x) as the sum, difference, product or quotient of two or more functions.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Determine the value of the composition of functions when evaluated at a point, including:

.

b. Determine, given the equations of two functions f(x) and g(x), the equation of the composite function: and explain any restrictions

c. Sketch, given the equations of two functions f(x) and g(x), the graph of the composite function: d. Write a function h(x) as the composition of two or more functions.

e. Write a function h(x) by combining two or more functions through operations on, and compositions of, functions

Demonstrate an understanding of factoring polynomials of degree greater than 2 (limited to polynomials of degree ≤ 5 with integral coefficients).

a. Explain how long division of a polynomial expression by a binomial expression of the form x − a, a∈ I , is related to synthetic division.

b. Divide a polynomial expression by a binomial expression of the form x − a, a∈ I , using long division or synthetic division.

c. Explain the relationship between the linear factors of a polynomial expression and the zeros of the corresponding polynomial function.

d. Explain the relationship between the remainder when a polynomial expression is divided by x − a, a∈ I , and the value of the polynomial expression at x = a (remainder theorem).

e. Explain and apply the factor theorem to express a polynomial expression as a product of factors.

Graph and analyze polynomial functions (limited to polynomial functions of degree ≤ 5 ).

a. Identify the polynomial functions in a set of functions, and explain the reasoning.

b. Explain the role of the constant term and leading coefficient in the equation of a polynomial function with respect to the graph of the function.

c. Generalize rules for graphing polynomial functions of odd or even degree.

d. Explain the relationship between: the zeros of a polynomial function the roots of the corresponding polynomial equation the x-intercepts of the graph of the polynomial function.

e. Explain how the multiplicity of a zero of a polynomial function affects the graph.

f. Sketch, with or without technology, the graph of a polynomial function.

g. Solve a problem by modelling a given situation with a polynomial function and analyzing the graph of the function.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Sketch the graph of a function that is the sum, difference, product or quotient of two functions, given their graphs.

b. Write the equation of a function that is the sum, difference, product or quotient of two or more functions, given their equations.

c. Determine the domain and range of a function that is the sum, difference, product or quotient of two functions.

d. Write a function h(x) as the sum, difference, product or quotient of two or more functions.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Determine the value of the composition of functions when evaluated at a point, including:

.

b. Determine, given the equations of two functions f(x) and g(x), the equation of the composite function: and explain any restrictions

c. Sketch, given the equations of two functions f(x) and g(x), the graph of the composite function: d. Write a function h(x) as the composition of two or more functions.

e. Write a function h(x) by combining two or more functions through operations on, and compositions of, functions

Demonstrate an understanding of factoring polynomials of degree greater than 2 (limited to polynomials of degree ≤ 5 with integral coefficients).

a. Explain how long division of a polynomial expression by a binomial expression of the form x − a, a∈ I , is related to synthetic division.

b. Divide a polynomial expression by a binomial expression of the form x − a, a∈ I , using long division or synthetic division.

c. Explain the relationship between the linear factors of a polynomial expression and the zeros of the corresponding polynomial function.

d. Explain the relationship between the remainder when a polynomial expression is divided by x − a, a∈ I , and the value of the polynomial expression at x = a (remainder theorem).

e. Explain and apply the factor theorem to express a polynomial expression as a product of factors.

Graph and analyze polynomial functions (limited to polynomial functions of degree ≤ 5 ).

a. Identify the polynomial functions in a set of functions, and explain the reasoning.

b. Explain the role of the constant term and leading coefficient in the equation of a polynomial function with respect to the graph of the function.

c. Generalize rules for graphing polynomial functions of odd or even degree.

d. Explain the relationship between: the zeros of a polynomial function the roots of the corresponding polynomial equation the x-intercepts of the graph of the polynomial function.

e. Explain how the multiplicity of a zero of a polynomial function affects the graph.

f. Sketch, with or without technology, the graph of a polynomial function.

g. Solve a problem by modelling a given situation with a polynomial function and analyzing the graph of the function.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Sketch the graph of a function that is the sum, difference, product or quotient of two functions, given their graphs.

b. Write the equation of a function that is the sum, difference, product or quotient of two or more functions, given their equations.

c. Determine the domain and range of a function that is the sum, difference, product or quotient of two functions.

d. Write a function h(x) as the sum, difference, product or quotient of two or more functions.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Determine the value of the composition of functions when evaluated at a point, including:

.

b. Determine, given the equations of two functions f(x) and g(x), the equation of the composite function: and explain any restrictions

c. Sketch, given the equations of two functions f(x) and g(x), the graph of the composite function: d. Write a function h(x) as the composition of two or more functions.

e. Write a function h(x) by combining two or more functions through operations on, and compositions of, functions

Demonstrate an understanding of factoring polynomials of degree greater than 2 (limited to polynomials of degree ≤ 5 with integral coefficients).

a. Explain how long division of a polynomial expression by a binomial expression of the form x − a, a∈ I , is related to synthetic division.

b. Divide a polynomial expression by a binomial expression of the form x − a, a∈ I , using long division or synthetic division.

c. Explain the relationship between the linear factors of a polynomial expression and the zeros of the corresponding polynomial function.

d. Explain the relationship between the remainder when a polynomial expression is divided by x − a, a∈ I , and the value of the polynomial expression at x = a (remainder theorem).

e. Explain and apply the factor theorem to express a polynomial expression as a product of factors.

Graph and analyze polynomial functions (limited to polynomial functions of degree ≤ 5 ).

a. Identify the polynomial functions in a set of functions, and explain the reasoning.

b. Explain the role of the constant term and leading coefficient in the equation of a polynomial function with respect to the graph of the function.

c. Generalize rules for graphing polynomial functions of odd or even degree.

d. Explain the relationship between: the zeros of a polynomial function the roots of the corresponding polynomial equation the x-intercepts of the graph of the polynomial function.

e. Explain how the multiplicity of a zero of a polynomial function affects the graph.

f. Sketch, with or without technology, the graph of a polynomial function.

g. Solve a problem by modelling a given situation with a polynomial function and analyzing the graph of the function.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Sketch the graph of a function that is the sum, difference, product or quotient of two functions, given their graphs.

b. Write the equation of a function that is the sum, difference, product or quotient of two or more functions, given their equations.

c. Determine the domain and range of a function that is the sum, difference, product or quotient of two functions.

d. Write a function h(x) as the sum, difference, product or quotient of two or more functions.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Determine the value of the composition of functions when evaluated at a point, including:

.

b. Determine, given the equations of two functions f(x) and g(x), the equation of the composite function: and explain any restrictions

c. Sketch, given the equations of two functions f(x) and g(x), the graph of the composite function: d. Write a function h(x) as the composition of two or more functions.

e. Write a function h(x) by combining two or more functions through operations on, and compositions of, functions

Demonstrate an understanding of factoring polynomials of degree greater than 2 (limited to polynomials of degree ≤ 5 with integral coefficients).

a. Explain how long division of a polynomial expression by a binomial expression of the form x − a, a∈ I , is related to synthetic division.

b. Divide a polynomial expression by a binomial expression of the form x − a, a∈ I , using long division or synthetic division.

c. Explain the relationship between the linear factors of a polynomial expression and the zeros of the corresponding polynomial function.

d. Explain the relationship between the remainder when a polynomial expression is divided by x − a, a∈ I , and the value of the polynomial expression at x = a (remainder theorem).

e. Explain and apply the factor theorem to express a polynomial expression as a product of factors.

Graph and analyze polynomial functions (limited to polynomial functions of degree ≤ 5 ).

a. Identify the polynomial functions in a set of functions, and explain the reasoning.

b. Explain the role of the constant term and leading coefficient in the equation of a polynomial function with respect to the graph of the function.

c. Generalize rules for graphing polynomial functions of odd or even degree.

d. Explain the relationship between: the zeros of a polynomial function the roots of the corresponding polynomial equation the x-intercepts of the graph of the polynomial function.

e. Explain how the multiplicity of a zero of a polynomial function affects the graph.

f. Sketch, with or without technology, the graph of a polynomial function.

g. Solve a problem by modelling a given situation with a polynomial function and analyzing the graph of the function.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Sketch the graph of a function that is the sum, difference, product or quotient of two functions, given their graphs.

b. Write the equation of a function that is the sum, difference, product or quotient of two or more functions, given their equations.

c. Determine the domain and range of a function that is the sum, difference, product or quotient of two functions.

d. Write a function h(x) as the sum, difference, product or quotient of two or more functions.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Determine the value of the composition of functions when evaluated at a point, including:

.

b. Determine, given the equations of two functions f(x) and g(x), the equation of the composite function: and explain any restrictions

c. Sketch, given the equations of two functions f(x) and g(x), the graph of the composite function: d. Write a function h(x) as the composition of two or more functions.

e. Write a function h(x) by combining two or more functions through operations on, and compositions of, functions

Demonstrate an understanding of factoring polynomials of degree greater than 2 (limited to polynomials of degree ≤ 5 with integral coefficients).

a. Explain how long division of a polynomial expression by a binomial expression of the form x − a, a∈ I , is related to synthetic division.

b. Divide a polynomial expression by a binomial expression of the form x − a, a∈ I , using long division or synthetic division.

c. Explain the relationship between the linear factors of a polynomial expression and the zeros of the corresponding polynomial function.

d. Explain the relationship between the remainder when a polynomial expression is divided by x − a, a∈ I , and the value of the polynomial expression at x = a (remainder theorem).

e. Explain and apply the factor theorem to express a polynomial expression as a product of factors.

Graph and analyze polynomial functions (limited to polynomial functions of degree ≤ 5 ).

a. Identify the polynomial functions in a set of functions, and explain the reasoning.

b. Explain the role of the constant term and leading coefficient in the equation of a polynomial function with respect to the graph of the function.

c. Generalize rules for graphing polynomial functions of odd or even degree.

d. Explain the relationship between: the zeros of a polynomial function the roots of the corresponding polynomial equation the x-intercepts of the graph of the polynomial function.

e. Explain how the multiplicity of a zero of a polynomial function affects the graph.

f. Sketch, with or without technology, the graph of a polynomial function.

g. Solve a problem by modelling a given situation with a polynomial function and analyzing the graph of the function.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Sketch the graph of a function that is the sum, difference, product or quotient of two functions, given their graphs.

b. Write the equation of a function that is the sum, difference, product or quotient of two or more functions, given their equations.

c. Determine the domain and range of a function that is the sum, difference, product or quotient of two functions.

d. Write a function h(x) as the sum, difference, product or quotient of two or more functions.

Demonstrate an understanding of operations on, and compositions of, functions.

a. Determine the value of the composition of functions when evaluated at a point, including:

.

b. Determine, given the equations of two functions f(x) and g(x), the equation of the composite function: and explain any restrictions

c. Sketch, given the equations of two functions f(x) and g(x), the graph of the composite function: d. Write a function h(x) as the composition of two or more functions.

e. Write a function h(x) by combining two or more functions through operations on, and compositions of, functions