Patterns and Functions Objectives 1 To write a

Patterns and Functions Objectives: (1) To write a function rule (2) To understand relationships of quantities in a function

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

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.

Example #1: Writing a Function Rule Let’s determine how much 1 shirt will cost. 8 x 1 shirt + 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

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 8 x + 25 Since “The Total Amount” = 8 x + 25, we’ll replace “The Total Amount” with y y = 8 x + 25 There’s your function rule!

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.

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.

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. a. 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.

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 0112.