• Explain the domain and range of a function. Under what circumstances would the domain be something other than all real numbers? Provide an example.

Domain: The domain of a function is the set of ‘input’ values; the function must be well defined for these input values. Range: The range of a function is the set of ‘output’ values that result after f is applied to every element of the domain.

**The domain will NOT be all real numbers when the horizontal distance from the origin is zero; Example: Consider the line of the form x=a, where a is any real number.
Here the domain is {a}, and the range is all real numbers. (x represents the horizontal distance from the origin)

• What is a function, in your own words? Give an example of a function using the variable x and explain how we evaluate a function for a given value of x.

Function: While the definition of a function is actually somewhat complex, we can summarize the basics as follows: If we were to take all possible values of x and plug them into the equation & solve for y, we will get exactly one value for each value of x

Example of a function: y = x2- 5x + 3
Evaluating a function: is simply asking what its value is for specific values of x; or what is the value of y when given the value of x. – plug in the value of x and then solve the equation for y.

...
all inputs are variable
3.1 The Production Function
Production function is a tool of analysis used in explaining the input-output relationship.
It describes the technical relationship between inputs and output in physical terms. In its
general form, it holds that production of a given commodity depends on certain specific
inputs. In its specific form, it presents the quantitative relationships between inputs and
outputs. A production function...

...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...

...difficult for both the assessor and the learner to judge what learning has taken place and then make any necessary adjustments to either complete the competency or develop the learning from where it was met
Students come to the classroom with a broad range of pre-existing knowledge, skills, beliefs, and attitudes, which influence how they attend, interpret and organize in-coming information. How they process and integrate new information will, in turn, affect how they remember,...

...1. Understand the principles and requirements of assessment
1.1Explain the function of assessment in learning and development
Assessment is carried out to ensure that learning has taken place. It measures the learner’s knowledge and skills in their learning area. Assessment encourages learners to ask questions on anything they have not fully understood, as learners know that they will have to prove their knowledge and understanding to the standards of the awarding body....

...1.1 Explain the function of assessment in learning and development.
Assessment is a way of finding out what learning has taken place. It enables the assessor to check what level of knowledge, skills and competency the candidate has throughout the qualification or programme. It starts with the assessor sitting down with the candidate at the beginning and creating an assessment plan for each stage of the candidate’s chosen course.
1.2 Define the key...

...variables
* Provide methods to get and set these variables
* Create another class TestPizza
* Initialize an instance of the class Pizza
* Set the fields of the instance with a value
* Output those fields with the use of getter functions
-------------------------------------------------
/***********************************************************************
The program TestPizza.java creates a class Pizza and defines methods to get and set...

...Graphs and Function
What is the relation between the graphs and function and how was it applied in the real world?
Graphs are frequently used in national magazines and newspaper to present information about things such as the world’s busiest airports (O’Hare in China is first, Heathrow in London is sixth), about the advertising-dollar receivers in the United States (newspaper are first, radio is fourth) and about NCAA men’s golf team title winner (Yael...

...CHAPTER 4 : FUNCTIONS AND THEIR GRAPHS
4.1 Definition of Function
A function from one set X to another set Y is a rule that assigns each element in X to one element in Y.
4.1.1 Notation
If f denotes a function from X to Y, we write
4.1.2 Domain and range
X is known as the domain of f and Y the range of f. (Note that domain and range are...

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