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

2. 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

3. 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

4. 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 }

5. Identifying a Function

6. 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.

7. 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 & 1.
This is NOT a function!

8. 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 &
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!

9. Identifying a Function: Graph
Example 1:
Does each x-value have only one y-value?
No! At 𝑥=0 (person), there are 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!

10. 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.

11. 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