Stage 5 Mathematics 3.0 Functions and Relations

In this section you will understand why some graphs are called functions and some are relations.

Big Ideas

3.1 To understand the vertical line test for a function

3.2 To be able to recognise a function from its equation

To Do This Lesson

Topic Rubric

Definition of Terms

Relation: Any set of ordered pairs LaTeX: (x,y) of real numbers.

Function: A relation between 2 sets where each element of one set associates with exactly one element in the second set

Vertical Line Test : If a vertical line is drawn anywhere across a graph and crosses the graph at two or more points for any value of LaTeX: x , then the graph is a relation.

One to One Correspondence: A graph where each value of LaTeX: x has only one LaTeX: y value. This graph would be a function.

One to Many Correspondence: A graph where each value of LaTeX: x will have a number of different LaTeX: y values. This graph would be a relation.

Many to One Correspondence: A graph where different values of LaTeX: x have the same LaTeX: y value. This graph would be a function.

Many to Many Correspondence: A graph where a number of values of LaTeX: x have a number of different LaTeX: y values. This graph would be a relation.

Open Ended Task

Notes and Video Instruction

Consolidation

Complete the following:

Complete the following task

Is this a function or a relation?

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