Pre-calculus Chapter 1 test Review
Calculators are allowed
Name:
I.D.:
Period:
1. Evaluate the function at each specified value of the independent variable and simplify
(a)
(b)
(c)
Find the difference quotient and simplify your answer
2.
3.
Use function notation to write g in terms of the common function f.
4.
5.
6.
.
7.
8.
Use a graphing utility to graph the function and determine whether the function is oneto-one. Explain the reason
9.
10.
11. Geometry A rectangular package to be sent by the U.S. Postal Service can have a
maximum combined length and girth (perimeter of a cross section) of 108 inches.
(a) Write the volume of the package as a function of x.
(b) What is the domain of the function?
(c) What dimensions will maximize the volume of the package?
12. The suggested retail price of a new car is p dollars. The dealership advertised a
factory rebate of $1200 and an 8% discount.
(a) Write a function R in terms of p, giving the cost of the car after receiving the rebate
from the factory.
(b) Write a function S in terms of p, giving the cost of the car after receiving the dealership
discount.
(c) Form the composite functions
and
and interpret each.
(d) Find
and
Which yields the lower cost for the car? Explain
13. Profit The profit P per week on a certain product is given by the model
where x is the amount spent on advertising. In this
model, x and P are both measured in hundreds of dollars.
(a) Use a graphing utility to graph the profit function.
(b) The business estimates that taxes and operating costs will increase by an average
of $2500 per week during the next year. Rewrite the profit equation to reflect this
expected decrease in profits. Identify the type of transformation applied to the graph of the
equation.
(c) Rewrite the profit equation so that x measures
advertising expenditures in
dollars. [Find Identify the type of transformation applied to the graph of the profit function
(a)
Find two functions f and g such that
answers.)
14.
15.
16.
17.
(There are many correct
Match the graph of the function with the graph of its inverse and explain the choice
(a)
(b)
(c)
18.
19.
20
.
Use the functions
21.
(1)
and
22.
(-2)
to find the specified functions.
23.
(3)
24.
(-4)