Module 7 Lesson 1

In this lesson, you will learn about relations and functions.

Module 7 - Lesson 1

Range

Domain

Quadrant

y-axis

x-axis

Coordinate Plane

OrderedPair

Origin

Lesson Vocabulary

relation

There are a few ways to tell if a relation is a function:Mapping DiagramsChecking the x-termsVertical Line Testand more!Every x-value must have ONE y-value.

Relations and Functions

Output

Input

15253545

10203040

{(10, 15), (20, 45), (30, 25), (40, 45)}

Ordered Pairs

Graph

Take a look at the various ways to write this relation.

Table

Domain: {10, 20, 30, 40}Range: {15, 25, 35, 45}

This relation is a function because each x-value maps to exactly ONE y-value.

Mapping

Relations and Functions

Output

Input

124

146

Table

Domain: {1, 2, 4}Range: {1, 4, 6}

This mapping is NOT a function because the x-value 2 has two different y-values.

Graph

Ordered Pair

{(2, 4), (4, 1), (2, 6), (1, 1)}

Mapping

Relations and Functions

You can use the vertical line test to determine if a graph is a function. If the vertical line only hits one point at a time then it is a function.

Function

Not a Function

Vertical Line Test

Test the graph for yourself. Graph the vertical line and drag it across the graph to determine if it is a function or not a function.

Vertical Line Test

Graphs

Video Explanations

Mapping and Ordered Pairs

You Try!

You Try!

The set of second numbers (y-values) of the ordered pairs in a relation.{(-1, 4), (0, 6), (5, -2)}R= {4, 6, -2}

x y

A set of numbers, or coordinates, written in the form (x, y).(-1, 5)

The four regions into which the x- and y-axis separate the coordinate plane.

(0, 0)

The point at which the x- and y-axis intersect on the coordinate plane; (0, 0).

y-axis

The vertical axis on a coordinate plane.

{(-1, 4), (0, 6), (5, -2)}D = {-1, 0, 5}

The set of first numbers (x-values) of the ordered pairs in a relation.

x-axis

The horizontal axis on a coordinate plane.

Formed by the intersection of two number lines, the horizontal axis and the vertical axis.