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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
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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