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Module 7 Lesson 1
High School
Created on November 20, 2024
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Transcript
Module 7 - Lesson 1
In this lesson, you will learn about relations and functions.
Lesson Vocabulary
Ordered Pair
Coordinate Plane
Origin
Domain
x-axis
y-axis
Quadrant
Range
Relations and Functions
There are a few ways to tell if a relation is a function:Mapping Diagrams Checking the x-terms Vertical Line Test and more! Every x-value must have ONE y-value.
relation
Relations and Functions
Mapping
Table
Graph
10 20 30 40
15 25 35 45
Input
Output
This relation is a function because each x-value maps to exactly ONE y-value.
Domain: {10, 20, 30, 40} Range: {15, 25, 35, 45}
Ordered Pairs
Take a look at the various ways to write this relation.
{(10, 15), (20, 45), (30, 25), (40, 45)}
Relations and Functions
Mapping
Graph
Table
1 4 6
1 2 4
Input
Output
This mapping is NOT a function because the x-value 2 has two different y-values.
Ordered Pair
Domain: {1, 2, 4} Range: {1, 4, 6}
{(2, 4), (4, 1), (2, 6), (1, 1)}
Vertical Line Test
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.
Not a Function
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.
Video Explanations
Mapping and Ordered Pairs
Graphs
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}
A set of numbers, or coordinates, written in the form (x, y). (-1, 5)
x y
The four regions into which the x- and y-axis separate the coordinate plane.
The point at which the x- and y-axis intersect on the coordinate plane; (0, 0).
(0, 0)
The vertical axis on a coordinate plane.
y-axis
The set of first numbers (x-values) of the ordered pairs in a relation.
{(-1, 4), (0, 6), (5, -2)} D = {-1, 0, 5}
The horizontal axis on a coordinate plane.
x-axis