Functions And Graphing Functions
Functions and graphing functions
Basics:
A function is a rule that changes input into output
A relation is any set of ordered pairs
A function is defined as a set of ordered pairs in which no two ordered pairs have the same element
A function must give exactly one unique output for each input
Also called a mapping or simply a map
The set of input numbers is called the domain
The set of output numbers is called the range
The set of all possible outputs is called the co-domain
The range is generally the subset of the co-domain however they can also be the same
Brackets:
A domain described as
That is, the square bracket means p is included. The rounded bracket means q is not included.
Number systems:
Composite functions:
When one function is followed by another function, the result is a composite function
Applying function after applying function is written in 3 different ways
All are pronounced ‘ after’ and mean ‘do followed by ’
Examples:
(i) Evaluate
(ii) Evaluate
(iii) Find the values for for which
(iv) Find
The number of people who visit a circus can be modelled by where represents theattendance of the circus days after it opens. The profit made by the circus can be modelled by where represents the profit in euros for the circus on a day when people attend
(i) Find the number of people who were in attendance on the fourth day
(ii) Find the profit made on the fourth day
(iii) Use these functions to find a new function that will give the profit made by the circus days after the circus opens
(iv) How much profit does the circus make on the third day
Graphing functions:
To graph a function, find points which satisfy the function by substituting values in for x (inputs) and finding the corresponding y values (outputs). Plot these points and join them up to obtain the graph of the function
Vertical line test:
If any imaginary vertical line cuts the graph at only one point then it is a function.
If any imaginary vertical line cuts the graph
Basics:
A function is a rule that changes input into output
A relation is any set of ordered pairs
A function is defined as a set of ordered pairs in which no two ordered pairs have the same element
A function must give exactly one unique output for each input
Also called a mapping or simply a map
The set of input numbers is called the domain
The set of output numbers is called the range
The set of all possible outputs is called the co-domain
The range is generally the subset of the co-domain however they can also be the same
Brackets:
A domain described as
That is, the square bracket means p is included. The rounded bracket means q is not included.
Number systems:
Composite functions:
When one function is followed by another function, the result is a composite function
Applying function after applying function is written in 3 different ways
All are pronounced ‘ after’ and mean ‘do followed by ’
Examples:
(i) Evaluate
(ii) Evaluate
(iii) Find the values for for which
(iv) Find
The number of people who visit a circus can be modelled by where represents theattendance of the circus days after it opens. The profit made by the circus can be modelled by where represents the profit in euros for the circus on a day when people attend
(i) Find the number of people who were in attendance on the fourth day
(ii) Find the profit made on the fourth day
(iii) Use these functions to find a new function that will give the profit made by the circus days after the circus opens
(iv) How much profit does the circus make on the third day
Graphing functions:
To graph a function, find points which satisfy the function by substituting values in for x (inputs) and finding the corresponding y values (outputs). Plot these points and join them up to obtain the graph of the function
Vertical line test:
If any imaginary vertical line cuts the graph at only one point then it is a function.
If any imaginary vertical line cuts the graph