Lesson 3.1How do we interpret and represent functions?

Concept: Intro to FunctionsEQ1: How do we determine if a relation is a function?

Standards F.IF. 1Vocabulary: Relation, Function, Vertical Line Test, Domain, Range

Suppose…Saturday you got a new video game for your X-Box 360. You played your new game for 3 hours on Saturday. You notice every time you press A, your player jumps. On Sunday, you play your game again. You press A. What do you expect your player to do?Your player does not jump, instead the player runs. Everything else works on the game so you continue to play.

SaturdayA jumps

SundayA runs

Continued….

On Monday you play your game again. When you press A what do you expect your player to do?Your player ducks. Are you willing to continue to play the game? Why or Why not? Monday

A ducks

Mapping

A jumpsrunsducks

Relation v.s. Function

Relation: a relationship between two sets of data

Examples:1. Neighbors on your block and the cars they drive

2. { (1, 2), (2, 3), (4, 5), (1,1)}3. x Y

0 21 42 6

Relation vs. FunctionFunction: a relationship between two sets of data where each input has only one output.Examples:1. Neighbors on your block and the cars they

drive (neighbor’s name is assigned to a make and model of a car) Neighbors Car

John

Susan

Mike

Jillian

Steve

Honda Accord

Chevy Silverado

Ford Focus

More Examples of Functions

2. { (1, 2), (2, 3), (4, 5), (6,8)}3. x Y

0 21 42 6

4.Domain – set of x-values that are valid for the function. AKA: Inputs

Range – set of y-values that are valid for the function.

Graphs of Functions

Vertical Line Test: an imaginary vertical line swept across the graph to see if the line ever crosses more than one point on the graph at the same time.• Function – crosses only one point on the

graph at the same time• NOT Function – crosses more than one point

on the graph at the same time

Function or Not?Use the vertical line test to determine if each relation is a function.

Determine if the following relations are functions. (You must provide a reason for your decision)

1. {(1, 3), (2, 6), (1, 5), (3, 8)}2. {(2, 4), (4, 8), (6, 12), (8, 16)}

3. d

4.

x Y-3 11 13 1

x Y2 12 53 1

5.

Think back to our beginning situation with the video game…..

1. Was our game defective? How do you know?2. How could we make our game a function?3. Can you think of other ways we use functions

in real life? How is a car like a function?4. What if pressing Z also made our player

jump? Would our game be a function? Explain your reasoning.