Relations and Functions, algebra homework help

Please complete the following questions. It is important that youshow all work you did to solve the problems when you submit your work.This includes any calculations, diagrams, or graphs that helped yousolve it.

Writing in Math Use the information onpage 115 to explain how step function’s apply to postage rates. Explainwhy a step function is the best model for this situation while your gasmileage as a function of time as you drive to the post office cannot bemodeled with a step function. Then graph the function that representsthe cost of a first-class letter.

Page 115 for question 4, will be attached in the attachment.

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 ($)
U.S.
1
0.39
0.63
MAL
2
3
0.87
New Vocabulary
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 function
greatest integer function
constant function
identity function
absolute value function
piecewise function
Study Tip
Greatest Integer
Function
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 r.
For example, (7.3] = 7 and [-1.5] = -2 because -1 > -1.5.
f(x) = [x]
A dot means that the
point is included in
the graph.
f(x)
X
f(x)
Notice that the domain
of this step function is
all real numbers and
the range is all
integers.
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