Lesson : Patterns and Functions

New VocabularyFunction

Function ruleDependent variable

Independent variableDomainRange

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 RuleThe 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

RelateDefine

WriteThe 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.

Memory

(mb)

Cost

($)

32 19

64 29

128 39

256 49

Cost of Memory Sticks

0 64 128 192 256 320

1020

3040

506070

Memory (megabytes)

Cos

t ($)

••

••

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. 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.

a. Identify the independent and dependent quantities for this situation.

b. 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.