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Math 1131 - Chap 1 Review
Free Response
1. If
, evaluate the difference quotient
.
2. Find the domain of the function.
3. Find the range of the function.
4. Find an expression for the function
whose graph is the bottom half of the parabola
5. A spherical balloon with radius r inches has volume
.
. Find a function that represents the amount of air
required to inflate the balloon from a radius of r inches to a radius of
inches.
6. An open rectangular box with volume 3 m3 has a square base. Express the surface area of the box as a
function S(x) of the length x of a side of the base.
7. Determine whether f is even, odd, or neither even nor odd.
8. In the function
, what is the value of d, if
?
9. Suppose that the graph of f is given. Describe how the graph of the function
from the graph of f.
can be obtained
10. If the point (7, 3) is on the graph of an even function, what other point must also be on the graph?
11. Use the table to evaluate the expression
x
f(x)
g(x)
1
3
6
2
2
5
3
1
2
4
0
3
.
5
1
4
6
2
6
12. Use the functions below to find a function g such that
If
and
.
.
13. Jason leaves Detroit at 3:00 P.M. and drives at a constant speed west along I-90. He passes Ann Arbor, 40 mi
from Detroit, at 3:30 P.M. The graph of the function of the distance traveled (in miles) in terms of the time
elapsed (in hours) is given below. Find the slope of the function.
14. The monthly cost of driving a car depends on the number of miles driven. Samantha found that in October it
cost her $312.5 to drive 500 mi and in February it cost her $375 to drive 1,000 mi.
Express the monthly cost C as a function of the distance driven d assuming that a linear relationship gives a
suitable model.
15. Find the inverse function of
16. If
, find
.
.
17. Find the exact value of the expression.
18. Solve each equation for .
a)
b)
19. Simplify the expression.
20. If
, find
.
21. Use the table to evaluate the expression
x
f(x)
g(x)
1
0
4
2
1
5
3
2
2
4
3
4
.
5
4
1
6
5
5
22. If a bacteria population starts with 100 bacteria and doubles every three hours, then the number of bacteria
after t hours is
. When will the population reach 50,000?
23. A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions
by
in. by cutting out equal squares of side x at each corner and then folding up the sides as in the
figure.
in.
Express the volume V of the box as a function of x.
24. Find the exponential function
whose graph is given.
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 25. Find the domain of the function.
Select the correct answer.
a.
b.
c.
d.
e.
____ 26. Suppose that the graph of f is given. Describe how the graph of the function
from the graph of f.
can be obtained
Select the correct answer.
a. Shift the graph 3 units to the right and 3 units down.
b. Shift the graph 3 units to the left and 3 units down.
c. Shift the graph 3 units to the right and 3 units up.
d. Shift the graph 3 units to the left and 3 units up.
e. none of these
____ 27. The table shows (lifetime) peptic ulcer rates (per 100 population) for various family incomes as reported by
the 1989 National Health Interview Survey.
Find the slope of the linear model using the first and last data points.
Number of data point
First
Second
Third
Fourth
Fifth
Ulcer rate (per 100 population)
14.3
13.8
14.2
13.5
12.3
Income
3,000
4,000
8,000
13,000
19,000
Select the correct answer.
a. 0.0005
b. 0.00008
c. 0.000125
d. 0.125
e. 1.5
____ 28. A study by the U.S. Office of Science and Technology in 1972 estimated the cost (in dollars) to reduce
automobile emissions by certain percentages and the graph gives the linear model of this table.
Reduction in
emissions (%)
50
55
60
65
70
Cost per car
(in $)
24
29.05
33.95
38.95
43.95
Find the cost, if the reduction in emissions is 80%, using this model.
Select the correct answer.
a. $63
b. $259
c. $44
d. $54
e. $70
____ 29. If
and
, find a function g such that
.
Select the correct answer.
a.
b.
c.
d.
e.
____ 30. What is
, given that
and
Select the correct answer.
a.
b.
c.
____ 31. For what values of x is the inequality true?
Select the correct answer to two decimal places.
a. (0, 0.75)
b. (0.85, 0)
c. (0.85, 0.85)
d.
e. (7.5, 0)
?