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 can be obtained from the graph of f.

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 / 1 / 2 / 3 / 4 / 5 / 6
f(x) / 3 / 2 / 1 / 0 / 1 / 2
g(x) / 6 / 5 / 2 / 3 / 4 / 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 / 1 / 2 / 3 / 4 / 5 / 6
f(x) / 0 / 1 / 2 / 3 / 4 / 5
g(x) / 4 / 5 / 2 / 4 / 1 / 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 in. by in. by cutting out equal squares of side x at each corner and then folding up the sides as in the figure.

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 can be obtained from the graph of f.

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 / Ulcer rate (per 100 population) / Income
First / 14.3 / 3,000
Second / 13.8 / 4,000
Third / 14.2 / 8,000
Fourth / 13.5 / 13,000
Fifth / 12.3 / 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 / Cost per car /
emissions (%) / (in $)
50 / 24
55 / 29.05
60 / 33.95
65 / 38.95
70 / 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)

Math 1131 - Chap 1 Review

Answer Section

FREE RESPONSE

1.ANS:

PTS:1

2.ANS:

PTS:1

3.ANS:

PTS:1

4.ANS:

PTS:1

5.ANS:

PTS:1

6.ANS:

PTS:1

7.ANS:

odd

PTS:1

8.ANS:

17

PTS:1

9.ANS:

Shift the graph 3 units to the right and 3 units down.

PTS:1

10.ANS:

(7, 3)

PTS:1

11.ANS:

2

PTS:1

12.ANS:

PTS:1

13.ANS:

80

PTS:1

14.ANS:

PTS:1

15.ANS:

PTS:1

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PTS:1

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PTS:1

18.ANS:

a) , b)

PTS:1

19.ANS:

PTS:1

20.ANS:

PTS:1

21.ANS:

4

PTS:1

22.ANS:

26.9 h

PTS:1

23.ANS:

PTS:1

24.ANS:

PTS:1

MULTIPLE CHOICE

25.ANS:DPTS:1

26.ANS:APTS:1

27.ANS:CPTS:1

28.ANS:DPTS:1

29.ANS:BPTS:1

30.ANS:APTS:1

31.ANS:CPTS:1