Holt Algebra 1

4-3 Writing Functions

Writing Functions

4-3

Holt Algebra 1

4-3 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

Step 1 List possible relationships between the first x and y-values.

5 – 4 = 1 and

Holt Algebra 1

4-3 Writing Functions

Example 1 Continued

Step 2 Determine which relationship works for the other x- and y- values.

10 – 4 2 and

15 – 4 3 and

20 – 4 4 and

The value of y is one-fifth, , of x.

Step 3 Write an equation.

or The value of y is one-fifth of x.

Holt Algebra 1

4-3 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

Step 1 List possible relationships between the first x- and y-values.

1 3 = 3 and 1 + 2 = 3

Holt Algebra 1

4-3 Writing Functions

y = 3x

Check It Out! Example 1 Continued

Step 2 Determine which relationship works for the other x- and y- values.

2 • 3 = 63 • 3 = 94 • 3 = 12

2 + 2 6 3 + 2 9 4 + 2 12

The value of y is 3 times x.

Step 3 Write an equation.

The value of y is 3 times x.

Holt Algebra 1

4-3 Writing Functions

The input (x-values) of a function is the independent variable. The output (y-values) 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.

Holt Algebra 1

4-3 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.

The amount of paint depends on the measurement of a room.

Dependent: amount of paintIndependent: measurement of the room

Holt Algebra 1

4-3 Writing Functions

Identify the independent and dependent variablesin the situation.

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

Dependent: height of candle Independent: time

The height of a candle depends on the number of hours it burns.

Example 2B: Identifying Independent and Dependent Variables

Holt Algebra 1

4-3 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)

Holt Algebra 1

4-3 Writing Functions

An algebraic expression that defines a function is a function rule.

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.

Holt Algebra 1

4-3 Writing Functions

The dependent variable is a function of the independent variable.

y = f(x)

Holt Algebra 1

4-3 Writing Functions

Identify the independent and dependent variables. Write a rule in function notation for the situation.

A math tutor charges $35 per hour.

The function for the amount a math tutor charges is f(h) = 35h.

Example 3A: Writing Functions

The amount a math tutor charges depends on number of hours.

Dependent: chargesIndependent: hours

Let h represent the number of hours of tutoring.

Holt Algebra 1

4-3 Writing Functions

You can think of a function as an input-output machine.

input

10

x

functionf(x)=5x

output

5x

6

30

2

Holt Algebra 1

4-3 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.

= 21 + 2

f(7) = 3(7) + 2 Substitute 7 for x.

f(x) = 3(x) + 2

= 23

Simplify.

f(x) = 3(x) + 2

f(–4) = 3(–4) + 2 Substitute –4 for x.Simplify.= –12 + 2

= –10

Holt Algebra 1

4-3 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.

Holt Algebra 1

4-3 Writing Functions

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

Ex. 5 A theater can be rented for exactly 2, 3, or 4 hours. The cost is a $100 deposit plus $200 per hour.

f(h) = 200h + 100Domain: {2, 3, 4}Range: {$500, $700, $900}

Holt Algebra 1

4-3 Writing Functions

H Dub• 4-3 Pg. 218 #11-15, 33-36, 40-45