Use the information on page 115 to explain how step function’s apply to postage rates. Explain why a step function is the best model for this situation while your gas mileage as a function of time as you drive to the post office cannot be modeled with a step function. Then graph the function that represents the cost of a first-class letter.Find page 115 attached2-6

Special Functions

GET READY for the Lesson

Main Ideas

• Identify and graph

step, constant, and

identity functions.

• Identify and graph

absolute value and

piecewise functions.

The cost of the postage to mail a letter

is a function of the weight of the letter.

But the function is not linear. It is a

special function called a step

function.

Weight not

over (ounces)

Price ($)

US.

MAL

1

2.

0.39

0.63

0.87

New Vocabulary

3

4

1.11

For letters with weights between

whole numbers, the cost “steps up” to

the next higher cost. So the cost to mail

a 1.5-ounce letter is the same as the cost

to mail a 2-ounce letter, $0.63.

step

greatest integer function

constant function

identity function

absolute value function

piecewise function

Study Tip

Step Functions, Constant Functions, and the Identity Function The

graph of a step function is not linear. It consists of line segments or rays.

The greatest integer function, written f(x) = [x], is an example of a step

function. The symbol [x] means the greatest integer less than or equal to x.

For example, [7.3] = 7 and [-1.5] = –2 because –1 > -1.5.

Greatest Integer

Function

f(x) = [x]

X

f(x)

Notice that the domain

of this step function is

all real numbers and

the range is all

integers.

A dot means that the

point is included in

the graph.

f(x)

-3

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