Lesson : Patterns and Functions New Vocabulary Function Function rule Dependent variable Independent variable Domain Range

Skill 1: Writing a Function Rule In Lesson 1-2, the equation C = p + 0.08p shows the relationship between the original price p of a pair of sneakers and the total cost C after the 8% sales tax is included. The relationship between these quantities is a function. The total cost depends on the original price. Relationships in which the output depends on the input are functions. A function rule, such as C = p + 0.08p, is an equation that describes a functional relationship.

Example 1: Writing a Function Rule Laundry Suppose you are washing and drying clothes at a self-service laundry. The relationship between the number of loads (input) and the cost (output) is a function. Use the table to write a function rule. Number of Loads 1 2 3 4 Cost $2.75 $5.50 $8.25 $11.00

Number of Loads 1 2 3 4 Cost $2.75 $5.50 $8.25 $11.00 Relate Define Write The function rule is

Quick Check 1. Write a function rule for the relationship between the number of hours (input) and the number of miles (output). Hours 1 2 3 4 Total Miles 60 120 180 240

Example 2: Writing a Function Rule The relationship between the number of houses (input) and the number of toothpicks (output) is a function. Use the table to write a function rule. Number of Houses 1 2 3 4 Total Number of Toothpicks 6 11 16 21 Relate Define Write The function rule is

Quick Check 2a. How many toothpicks are needed to make seven houses? b. Reasoning Could a set of houses be built with exactly 12 toothpicks? Explain. c. Write a rule for the function represented by the data in the table. Input x 1 2 3 4 Output y 5 8 11 14

Skill 2: Relationships in a Function In example 2, the total number of toothpicks t depends on the number of houses n. The value of the dependent variable t depends on the value of the independent variable n. In real-world situations, you must determine which varying quantity is dependent and which is independent.

Example 3: Identifying Independent and Dependent Quantities Memory Stick The table and graph model a function relating the storage capacity of a memory stick and its cost. Identify the independent and dependent quantities. Cost of Memory Sticks Memory (mb) Cost ($) 32 19 64 29 128 39 256 49 70 60 • 50 • 40 Cost ($) 30 • • 20 10 64 128 192 256 320 Memory (megabytes)

Quick Check 3. The cooking time for an unstuffed turkey is about 20 minutes per pound. What are the independent quantity and dependent quantity for this situation?

A function assigns exactly one output value for each input value A function assigns exactly one output value for each input value. The possible values for the input, or the independent variable, of a function are the domain of the function. The possible values of the output, or the dependent variable, are the range of the function

Example 4: Reasonable Domain and Range Maria earns $7 per hour for baby-sitting after school and on Saturday. She works no more than 16 hours a week. Identify the independent and dependent quantities for this situation. Find reasonable domain and range values for this situation.

Quick Check 4. Charlie downloads songs for $0.75 each. He has between $3.00 and $6.00 to spend on songs. Identify the independent and dependent quantities for this situation and find reasonable domain and range values.