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Holt McDougal Algebra 1 Writing Functions Writing Functions Holt Algebra 1 Unit 3 Unit 3 Module 8 Module 8 Lesson 3 Lesson 3 Holt McDougal Algebra 1

Holt McDougal Algebra 1 Writing Functions Holt Algebra 1 Unit 3 Unit 3 Module 8 Module 8 Lesson 3 Lesson 3 Holt McDougal Algebra 1

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Page 1: Holt McDougal Algebra 1 Writing Functions Holt Algebra 1 Unit 3 Unit 3 Module 8 Module 8 Lesson 3 Lesson 3 Holt McDougal Algebra 1

Holt McDougal Algebra 1

Writing FunctionsWriting Functions

Holt Algebra 1

Unit 3Unit 3

Module 8Module 8

Lesson 3Lesson 3

Holt McDougal Algebra 1

Page 2: Holt McDougal Algebra 1 Writing Functions Holt Algebra 1 Unit 3 Unit 3 Module 8 Module 8 Lesson 3 Lesson 3 Holt McDougal Algebra 1

Holt McDougal Algebra 1

Writing Functions

Identify independent and dependent variables.

Write an equation in function notation and evaluate a function for given input values.

Objectives

Page 3: Holt McDougal Algebra 1 Writing Functions Holt Algebra 1 Unit 3 Unit 3 Module 8 Module 8 Lesson 3 Lesson 3 Holt McDougal Algebra 1

Holt McDougal Algebra 1

Writing Functions

independent variabledependent variablefunction rule function notation

Vocabulary

Page 4: Holt McDougal Algebra 1 Writing Functions Holt Algebra 1 Unit 3 Unit 3 Module 8 Module 8 Lesson 3 Lesson 3 Holt McDougal Algebra 1

Holt McDougal Algebra 1

Writing Functions

Example 1: Using a Table to Write an Equation

Determine a relationship between the x- and y-values. Write an equation.

x

y

5 10 15 20

1 2 3 4

Page 5: Holt McDougal Algebra 1 Writing Functions Holt Algebra 1 Unit 3 Unit 3 Module 8 Module 8 Lesson 3 Lesson 3 Holt McDougal Algebra 1

Holt McDougal Algebra 1

Writing Functions

Check It Out! Example 1

Determine a relationship between the x- and y-values. Write an equation.

{(1, 3), (2, 6), (3, 9), (4, 12)}

x

y

1 2 3 4

3 6 9 12

Page 6: Holt McDougal Algebra 1 Writing Functions Holt Algebra 1 Unit 3 Unit 3 Module 8 Module 8 Lesson 3 Lesson 3 Holt McDougal Algebra 1

Holt McDougal Algebra 1

Writing Functions

The equation in Example 1 describes a function because for each x-value (input), there is only one y-value (output).

Page 7: Holt McDougal Algebra 1 Writing Functions Holt Algebra 1 Unit 3 Unit 3 Module 8 Module 8 Lesson 3 Lesson 3 Holt McDougal Algebra 1

Holt McDougal Algebra 1

Writing Functions

The input of a function is the independent variable. The output of a function is the dependent variable. The value of the dependent variable depends on, or is a function of, the value of the independent variable.

Page 8: Holt McDougal Algebra 1 Writing Functions Holt Algebra 1 Unit 3 Unit 3 Module 8 Module 8 Lesson 3 Lesson 3 Holt McDougal Algebra 1

Holt McDougal Algebra 1

Writing Functions

Example 2A: Identifying Independent and Dependent Variables

Identify the independent and dependent variablesin the situation.

A painter must measure a room before deciding how much paint to buy.

Page 9: Holt McDougal Algebra 1 Writing Functions Holt Algebra 1 Unit 3 Unit 3 Module 8 Module 8 Lesson 3 Lesson 3 Holt McDougal Algebra 1

Holt McDougal Algebra 1

Writing Functions

Identify the independent and dependent variablesin the situation.

The height of a candle decreases d centimeters for every hour it burns.

Example 2B: Identifying Independent and Dependent Variables

Page 10: Holt McDougal Algebra 1 Writing Functions Holt Algebra 1 Unit 3 Unit 3 Module 8 Module 8 Lesson 3 Lesson 3 Holt McDougal Algebra 1

Holt McDougal Algebra 1

Writing Functions

A veterinarian must weigh an animal before determining the amount of medication.

Identify the independent and dependent variablesin the situation.

Example 2C: Identifying Independent and Dependent Variables

Page 11: Holt McDougal Algebra 1 Writing Functions Holt Algebra 1 Unit 3 Unit 3 Module 8 Module 8 Lesson 3 Lesson 3 Holt McDougal Algebra 1

Holt McDougal Algebra 1

Writing Functions

Helpful Hint

There are several different ways to describe the variables of a function.

IndependentVariable

DependentVariable

x-values y-values

Domain Range

Input Output

x f(x)

Page 12: Holt McDougal Algebra 1 Writing Functions Holt Algebra 1 Unit 3 Unit 3 Module 8 Module 8 Lesson 3 Lesson 3 Holt McDougal Algebra 1

Holt McDougal Algebra 1

Writing Functions

Check It Out! Example 2a

A company charges $10 per hour to rent a jackhammer.

Identify the independent and dependent variable in the situation.

Page 13: Holt McDougal Algebra 1 Writing Functions Holt Algebra 1 Unit 3 Unit 3 Module 8 Module 8 Lesson 3 Lesson 3 Holt McDougal Algebra 1

Holt McDougal Algebra 1

Writing Functions

Identify the independent and dependent variable in the situation.

Check It Out! Example 2b

Apples cost $0.99 per pound.

Page 14: Holt McDougal Algebra 1 Writing Functions Holt Algebra 1 Unit 3 Unit 3 Module 8 Module 8 Lesson 3 Lesson 3 Holt McDougal Algebra 1

Holt McDougal Algebra 1

Writing Functions

An algebraic expression that defines a function is a function rule. Suppose Tasha earns $5 for each hour she baby-sits. Then 5 • x is a function rule that models her earnings.

If x is the independent variable and y is the dependent variable, then function notation for y is f(x), read “f of x,” where f names the function. When an equation in two variables describes a function, you can use function notation to write it.

Page 15: Holt McDougal Algebra 1 Writing Functions Holt Algebra 1 Unit 3 Unit 3 Module 8 Module 8 Lesson 3 Lesson 3 Holt McDougal Algebra 1

Holt McDougal Algebra 1

Writing Functions

The dependent variable is a function of the independent variable.

y is a function of x.

y = f (x)

y = f(x)

Page 16: Holt McDougal Algebra 1 Writing Functions Holt Algebra 1 Unit 3 Unit 3 Module 8 Module 8 Lesson 3 Lesson 3 Holt McDougal Algebra 1

Holt McDougal Algebra 1

Writing Functions

Identify the independent and dependent variables. Write an equation in function notation for the situation.

A math tutor charges $35 per hour.

Example 3A: Writing Functions

Page 17: Holt McDougal Algebra 1 Writing Functions Holt Algebra 1 Unit 3 Unit 3 Module 8 Module 8 Lesson 3 Lesson 3 Holt McDougal Algebra 1

Holt McDougal Algebra 1

Writing Functions

A fitness center charges a $100 initiation fee plus $40 per month.

Example 3B: Writing Functions

Identify the independent and dependent variables. Write an equation in function notation for the situation.

Page 18: Holt McDougal Algebra 1 Writing Functions Holt Algebra 1 Unit 3 Unit 3 Module 8 Module 8 Lesson 3 Lesson 3 Holt McDougal Algebra 1

Holt McDougal Algebra 1

Writing Functions

Check It Out! Example 3a

Identify the independent and dependent variables. Write an equation in function notation for the situation.

Steven buys lettuce that costs $1.69/lb.

Page 19: Holt McDougal Algebra 1 Writing Functions Holt Algebra 1 Unit 3 Unit 3 Module 8 Module 8 Lesson 3 Lesson 3 Holt McDougal Algebra 1

Holt McDougal Algebra 1

Writing Functions

Check It Out! Example 3bIdentify the independent and dependent variables. Write an equation in function notation for the situation.

An amusement park charges a $6.00 parking fee plus $29.99 per person.

Page 20: Holt McDougal Algebra 1 Writing Functions Holt Algebra 1 Unit 3 Unit 3 Module 8 Module 8 Lesson 3 Lesson 3 Holt McDougal Algebra 1

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Writing Functions

You can think of a function as an input-output machine. For Tasha’s earnings, f(x) = 5x. If you input a value x, the output is 5x.

input

10

x

functionf(x)=5x

output

5x

6

30

2

Page 21: Holt McDougal Algebra 1 Writing Functions Holt Algebra 1 Unit 3 Unit 3 Module 8 Module 8 Lesson 3 Lesson 3 Holt McDougal Algebra 1

Holt McDougal Algebra 1

Writing Functions

Example 4A: Evaluating Functions

Evaluate the function for the given input values.

For f(x) = 3x + 2, find f(x) when x = 7 and when x = –4.

Page 22: Holt McDougal Algebra 1 Writing Functions Holt Algebra 1 Unit 3 Unit 3 Module 8 Module 8 Lesson 3 Lesson 3 Holt McDougal Algebra 1

Holt McDougal Algebra 1

Writing Functions

Example 4B: Evaluating Functions

Evaluate the function for the given input values.

For g(t) = 1.5t – 5, find g(t) when t = 6 and when t = –2.

Page 23: Holt McDougal Algebra 1 Writing Functions Holt Algebra 1 Unit 3 Unit 3 Module 8 Module 8 Lesson 3 Lesson 3 Holt McDougal Algebra 1

Holt McDougal Algebra 1

Writing Functions

Example 4C: Evaluating Functions

Evaluate the function for the given input values.

For , find h(r) when r = 600

and when r = –12.

Page 24: Holt McDougal Algebra 1 Writing Functions Holt Algebra 1 Unit 3 Unit 3 Module 8 Module 8 Lesson 3 Lesson 3 Holt McDougal Algebra 1

Holt McDougal Algebra 1

Writing Functions

Check It Out! Example 4a

Evaluate the function for the given input values.

For h(c) = 2c – 1, find h(c) when c = 1 and when c = –3.

Page 25: Holt McDougal Algebra 1 Writing Functions Holt Algebra 1 Unit 3 Unit 3 Module 8 Module 8 Lesson 3 Lesson 3 Holt McDougal Algebra 1

Holt McDougal Algebra 1

Writing Functions

Check It Out! Example 4b

Evaluate the function for the given input values.

For g(t) = , find g(t) when t = –24 and

when t = 400.

Page 26: Holt McDougal Algebra 1 Writing Functions Holt Algebra 1 Unit 3 Unit 3 Module 8 Module 8 Lesson 3 Lesson 3 Holt McDougal Algebra 1

Holt McDougal Algebra 1

Writing Functions

When a function describes a real-world situation, every real number is not always reasonable for the domain and range. For example, a number representing the length of an object cannot be negative, and only whole numbers can represent a number of people.

Page 27: Holt McDougal Algebra 1 Writing Functions Holt Algebra 1 Unit 3 Unit 3 Module 8 Module 8 Lesson 3 Lesson 3 Holt McDougal Algebra 1

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Example 5: Finding the Reasonable Domain and Range of a Function

Write a function to describe the situation. Find the reasonable domain and range of the function.

Joe has enough money to buy 1, 2, or 3 DVDs at $15.00 each, if he buys any at all.

Page 28: Holt McDougal Algebra 1 Writing Functions Holt Algebra 1 Unit 3 Unit 3 Module 8 Module 8 Lesson 3 Lesson 3 Holt McDougal Algebra 1

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Writing Functions

Check It Out! Example 5

The settings on a space heater are the whole numbers from 0 to 3. The total number of watts used for each setting is 500 times the setting number. Write a function to describe the number of watts used for each setting. Find the reasonable domain and range for the function.

Page 29: Holt McDougal Algebra 1 Writing Functions Holt Algebra 1 Unit 3 Unit 3 Module 8 Module 8 Lesson 3 Lesson 3 Holt McDougal Algebra 1

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Writing Functions

Homework

Pg. 207-209

15-26 all, 28-38 even