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MULTIPLE CHOICE
1. Determine the domain and range of the piecewise function. 1. ______
A. Domain [–2, 4]; Range [–3, 3]
B. Domain [–3, 3]; Range [0, 3]
C. Domain [–3, 3]; Range [–2, 4]
D. Domain [–1, 4]; Range [–2, 2]
-2
2
4
-4
-2
2. Solve:
17 3x x+ = - 2. ______
A. No solution
B. -1, 8
C. -1
D. 8
3. Determine the interval(s) on which the function is decreasing.
3. ______
A.
( )
, 0-8 and
( )
2, 8
B.
( )
, 5/ 3-8 - ,
( )
0, 2 , and
( )
11/ 3, 8
C.
( )
1,1- and
( )
3, 8
D.
( )
, 4 / 3-8
4. Determine whether the graph of
xy = is symmetric with respect to the origin,
the
x-axis, or the y-axis. 4. ______
A. symmetric with respect to the x-axis only
B. symmetric with respect to the
y-axis only
C. symmetric with respect to the origin only
D. not symmetric with respect to the x-axis, not symmetric with respect to the y-axis, and
not symmetric with respect to the origin
5. Solve, and express the answer in interval notation:
| 8 – 3x | = 20. 5. ______
A. (–8, 28/3] ∪ [– 4, 8)
B. [– 4, 28/3]
C. (–8, – 4]
D. (–8, – 4] ∪ [28/3, 8)
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6. Which of the following represents the graph of 9
x - 4y = 36 ? 6. ______
A. B.
C. D.
7. Write a slope-intercept equation for a line parallel to the line
x + 3y = 8 which passes through
the point (– 4, 5). 7. ______
8. Which of the following best describes the graph? 8. ______
A. It is the graph of a one-to-one function.
B. It is the graph of a function but not one-to-one.
C. It is a parabolic graph.
D. It is not the graph of a function.
9. Express as an equivalent expression: log x + log 1 – 8 log (y + 2) 9. ______
10. Which of the functions corresponds to the graph? 10. ______
11. Suppose that for a function f , the equation f (x) = 0 has exactly three real-number solutions.
Which of the following statements MUST be true? 11. ______
A. f has exactly three x-intercepts.
B. f has exactly three y-intercepts.
C. f is a polynomial of degree 3.
D. f is an invertible function.
12. The graph of y = f
(x) is shown at the left and the graph of y = g(x) is shown at the right. (No
formulas are given.) What is the relationship between g(x) and f (x)?
SHORT ANSWER:
13. Multiply and simplify: (7 + 2i).
Write the answer in the form a + bi, where a and b are real numbers. Answer: ________
14. Solve, and write the answer in interval notation:
15. Water initially at 130° F. is left in a room of temperature 70° F to cool.
After t minutes, the temperature T of the water is given by
Find the temperature of the water 12 minutes after it is left to cool. (Round to the nearest degree.)
16. Find the value of the logarithm:
17. Solve:
6 1
x-
9 81
18. Suppose $7,000 is invested in an account at an annual interest rate of 2.3% compounded
continuously. How long (to the nearest tenth of a year) will it take the investment to double in
size?
19. Let f (x) = x
2
+ 10x + 32.
(a) Find the vertex. Answer: ________
(b) State the range of the function. Answer: ________
(c) On what interval is the function decreasing? Answer: ________
20. Consider the polynomial P(x), shown in both standard form and factored form.
1 7 7 1
( ) 3 ( 1)( 3)( 5)
3 2
5 5 5 5
P x x x x x x x= - + - - = - + - -
(a) Which sketch illustrates the end behavior of the polynomial function?
Answer: ________
(b) State the zeros of the function. Answer: ________________
(c) State the y-intercept. Answer: ________________
(d) State which graph below is the graph of P(x). Answer: ________
GRAPH A GRAPH B
(a) State the domain. Answer: _________________
(b) State the horizontal asymptote. Answer: _________________
(c) State the vertical asymptote(s).
(d) Which of the following represents the graph of
GRAPH C. GRAPH D.
SHORT ANSWER, with work required to be shown, as indicated.
22. Let f (x) = x + 2 and xxg -= 9)( .
(a) Find )7(
. Show work.
(b) Find the domain of the quotient function
23. Points (–1, 2) and (9, 4) are endpoints of the diameter of a circle.
(a) What is the length of the diameter? Give the exact answer, simplified as much as possible.
Show work.
(b) What is the center point C of the circle?
(c) Given the point C you found in part (b), state the point symmetric to C about the y-axis.
24. Find the equation for a line which passes through the points (3, 7) and (6, 1). Write the
equation in slope-intercept form.
Show work.
25. Sam, a resident of Metropolis, pays Metropolis an annual tax of $75 plus 1.6% of his annual
income. If Sam paid $1,171 in tax, what was Sam’s income?
Show work.
26. Let
f (x) = 2x
2 + 7 and g(x) = x – 4.
(a) Find the composite function ))(( xgf o and simplify. Show work.
(b) Find
( )
( 1)f g -o . Show work.
27. Find the exact solutions and simplify as much as possible: 10
28. Given the function
+ 9 = 20x. Show work.
f x x= + , find a formula for the inverse function. Show work.
29. Lee’s Bakery has determined that when
x chocolate cakes are made daily, the average cost
per chocolate cake, in dollars, is given by
C(x) = 0.001 x
2
– 0.13x + 12.20
(a) What is the average cost per cake if 40 chocolate cakes are made daily?
(b) How many chocolate cakes should be made daily in order to minimize the average cost per
cake?
Show work.
