1. Patterns and Functions
Objectives:
To write a function rule
To understand relationships of quantities in a function

2. Definitions
Function: a relationship that assign exactly one output value for each input value.
Function Rule: an equation that describes a functional relationship.

3. Example #1: Writing a Function Rule
T-Shirts: Joe wants to order t-shirts for his A Capella band, “The Sly Voxes.” He goes to US Shirts and finds out there is a $25 set up fee. Also, each shirt will cost $8. Write a function rule the represents the cost of the shirts.

4. Example #1: Writing a Function Rule
Let’s determine how much 1 shirt will cost. 8 x 1shirt + 25 for setup 8(1) + 25 = 33 Now, let determine how much 2 shirts will cost. 8(2) + 25 = 41 3 shirts? 10 shirts? 8(3) + 25 = 49 8(10) + 25 = 105

5. Example #1: Writing a Function Rule
Can we say that the total price is: 8 x (number of shirts) + 25? Then replace the words “number of shirts” with a variable 8x + 25 Since “The Total Amount” = 8x + 25, we’ll replace “The Total Amount” with y y = 8x + 25 There’s your function rule!

6. Relationships in a Function
Dependent Variable: The variable who’s value depends on what the other variable is.
Independent Variable: The variable that can be freely chosen within certain bounds.
Ex: Total Cost depends on the number of items your buy.
Ex: Weekly pay depends on the number of hours worked.

7. Relationships in a Function (continued)
Domain: The possible values for the input, or the independent variable. Range: The possible values for the output, or the dependent variable.

8. Example #2: Reasonable Domain and Range
Maria earns $7 per hour for baby-sitting after school and on Saturdays. She works no more than 16 hours a week.
Identify the independent and dependent quantities for this situation.
The amount Maria earns depends on the number of hours she works in a week. So the amount Maria earns is the dependent variable. The number of hours she works is the independent variable.

9. Example #2: Reasonable Domain and Range (continued)
b. Find reasonable domain and range valued for this situation.
A reasonable domain is from 0-16 hours. If Maria works 0 hours, she earns $0. If she works 16 hours, she earns $112. A reasonable range would be