Topic 3: Relations, Functions, Function Behavior Lesson 15 (1.7) Algebra 1

Learning Targets Define a function and function notation Identify a function from a table, ordered pairs, graph, equation, and mapping diagram Identify a function using the vertical line test Construct a function in a table, ordered pairs, graph, and mapping diagram Determine the domain and range of a function from a table, ordered pairs, graph, and mapping diagram Graph a function by creating a table Determine function values from an equation Determine the meaning of function components in a context

Function Example: Each person has only one birthday Definition: a specific type of relation where each input has EXACTLY ONE output. Non-Example: March 15th is multiple people’s birthday Representations: Table, graph, ordered pairs, equation, mapping diagram

Function Representations Mapping Diagram Equation Table Graph 𝑓 𝑥 = 𝑥 2 X Y -1 1 2 4 -1 1 2 1 4 Ordered Pairs { −1, 1 , 0, 0 , 1, 1 , 2, 4 }

Identifying a Function 1 2 3 4 5 6 7 8

Identifying a Function: Ordered Pairs Example 1: Does each x-value only have 1 y-value? Yes! Each x-value (person) has only one specific y-value (birthday) This is a function! Example 2: This example is like quadruplets having the same birthday. They may all have the same birthday, but each person only has one birthday.

Identifying a Function: Mapping Diagram Example 1: Does each x-value have only 1 y-value? Yes! Each x-value (person) has only one y-value (birthday). This is a function! Example 2: Does each x-value have only 1 y-value? No! The x-value -1 (person) has two y-values (birthday) of -6 & 1. This is NOT a function!

Identifying a Function: Table Example 1: Does each x-value have only 1 y-value? No! The x-value -3 (person) has two different y-values (birthday) of 8 & -1. This is NOT a function! Example 2: Does each x-value have only 1 y-value? Yes! Each x-value (person) has only one y-value (birthday). This is a function!

Identifying a Function: Graph Example 1: Does each x-value have only one y-value? No! At 𝑥=0 (person), there are 2 y-values (birthday) of 𝑦=−5, 3 This is NOT a function! Example 2: Does each x-value have only one y-value? Yes! Each x-value (person) has only one y-value (birthday). This is a function!

Vertical Line Test Examples: To help us identify the graph of a function, we can use the vertical line test. It helps us ensure that for every x value there is only one y-value.

Exit Ticket for Feedback 1. What is the definition of a function in your own words. 2. Create an example of a function in a mapping diagram. 3. Create an example of a relation that is not a function in a table. Google Survey: tinyurl.com/Unit1-L15