Lesson 3. 1 How do we interpret and represent functions Lesson 3.1 How do we interpret and represent functions? Concept: Intro to Functions EQ1: How do we determine if a relation is a function? Standards F.IF. 1 Vocabulary: Relation, Function, Vertical Line Test, Domain, Range

Suppose… Saturday you got a new video game for your Xbox One Suppose… Saturday you got a new video game for your Xbox One. 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. Saturday A jumps This is a launch activity to get students thinking about the role of the input and output. Sunday A 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 After students have had time to discuss their answers. Point out how pressing the same button should give you the same result. If you press the same button and get a different result are you able to play the game? Mapping A jumps runs ducks

Relation v.s. Function Relation: a relationship between two sets of data Examples: Neighbors on your block and the cars they drive { (1, 2), (2, 3), (4, 5), (1,1)} x Y 2 1 4 6

Relation vs. Function Function: a relationship between two sets of data where each input has only one output. Examples: 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 Honda Accord Chevy Silverado Ford Focus Mike Jillian Steve

More Examples of Functions 2. { (1, 2), (2, 3), (4, 5), (6,8)} 3. x Y 2 1 4 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. AKA:Outputs

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.

{(1, 3), (2, 6), (1, 5), (3, 8)} {(2, 4), (4, 8), (6, 12), (8, 16)} Determine if the following relations are functions. (You must provide a reason for your decision) {(1, 3), (2, 6), (1, 5), (3, 8)} {(2, 4), (4, 8), (6, 12), (8, 16)} d x Y -3 1 3 5. You may need to give some additional classwork. x Y 2 1 5 3

Think back to our beginning situation with the video game….. Was our game defective? How do you know? How could we make our game a function? Can you think of other ways we use functions in real life? How is a car like a function? What if pressing Z also made our player jump? Would our game be a function? Explain your reasoning. Yes, every time I pressed A, I got a different answer. Our game could be a function if pressing A yielded the same result or every time you press A you jump. Allow students to respond Yes our game would be a function because each input has only one output.