Transcribed Text
1. Determine the domain and range of the piecewise function.
1.
4
2
4
2
2
4
2
4
A.
Domain [4, 2]; Range [3, 3]
B.
Domain [4, 2]; Range [2, 1]
C.
Domain [2, 1]; Range I4, 2]
D.
Domain [3, 3]; Range I4, 2]
2. Solve: /x+17=3x 
2.
A. 7
B. 1
C.  1, 8
D.
3. Determine the interval(s) on which the function is increasing.
3.
A. (1,1) and (3,00)
4
B. (4/3, 1)
2
C. (00,5/3), (0,2), and (11/3,00)
D. (00,0) and (2,00)
2
4
2
4. Determine whether the graph of = is symmetric with respect to the origin,
the xaxis, or the yaxis.
4.
A. not symmetric with respect to the xaxis, not symmetric with respect to the yaxis, and
not symmetric with respect to the origin
B.
symmetric with respect to the xaxis only
C.
symmetric with respect to the yaxis only
D.
symmetric with respect to the origin only
5. Solve, and express the answer in interval notation: 165xl<14. 
5.
A.
[8/5, 4]
B.
(00, 8/5] U [4, 00)
C. (00,8/5]
D. [4,00)
6. Which of the following represents the graph of 4x  7y=28?
6.
A.
B.
10
10
5
5
10
5.
10
10
5.
5
10
10
10
C.
D.
10
10
5
5
10
5
10
10
5
5
10
5
10
10
7. Write a slopeintercept equation for a line parallel to the line x+ 5y = 7 which passes through
the point (10, 3).
7.
A. y =5x+53
B. y 5 1
1
C. y= 5
D. >==x+5 1
8. Does the graph below represent a function and is it onetoone?
8.
4
2
T
A. It is a function and it is onetoone.
B. It is a function but not onetoone.
C. It is not a function but it is onetoone.
D. It is not a function and it is not onetoone.
9. Express as an equivalent logarithm: log + log 1  8log (y+2)
9.
x+1
A. log
8(y+2)
B.
log x
log(y+2)
x
C. log
8
(y+2)
D. log (x8y15)
10. Which of the functions corresponds to the graph?
10.
8
6
4+
2
2
2
4
6
A. f (x) = ex +2
B. f f(x)=ex (x) e*+2
=
C. +2
D. f(x)=e**+1 =
11. Suppose that a function f has no xintercepts.
Which of the following statements MUST be true?
11.
A.
f is an invertible function.
B.
The graph of f has no points whose xcoordinate is 0.
C.
The graph of f is a horizontal line.
D.
The equation f (x) = 0 has no realnumber solution.
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)?
12.
4
4
2
2
4
2
2
4
4
2
2
4
2
2
4
4
y = f(x)
y=g(x)
A. g(x=f(x2)1 :
B.
g(x) =f(x+1)2 = 
C.
g(x) =f(x+2)1 =
D.
g(x) = f(x + 2) + 2
SHORT ANSWER:
13. Multiply and simplify: (3 + 8i)(5 + 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:
x6 >0.
Answer:
x8
15. A can of soda at 82° F. is placed in a refrigerator that maintains a constant temperature of 35°
F. The temperature T of the soda t minutes after it is placed in the refrigerator is given by

t
Find the temperature of the soda 10 minutes after it is placed in the refrigerator. (Round to the
nearest tenth of a degree.)
Answer:
16.
Find the value of the logarithm: logs (3)
Answer:
17. Solve: 35x2=9.
Answer:
18. Suppose $7,800 is invested in an account at an annual interest rate of 4.3% compounded
continuously. How long (to the nearest tenth of a year) will it take the investment to double in
size?
Answer:
19. Let f (x) = x2  4x 
(a) Find the vertex.
Answer:
(b) State the range of the function.
Answer:
(c) On what interval is the function decreasing?
20. Consider the polynomial P(x), shown in both standard form and factored form.
1
1
7
41
1
P(x) = + + x x+3 = (x+3)(xD/x2)(x5)
10
2
10
10
10
(a) Which sketch illustrates the end behavior of the polynomial function?
A.
B.
C.
D.
ww
Answer:
(b) State the yintercept.
Answer:
(c) State the zeros of the function.
Answer:
(d) State which graph below is the graph of P(x).
Answer:
GRAPH A
GRAPH B
10
10
5.
4
4
2
5
5
10
10
GRAPH C
GRAPH D
10
10
5
5
4
2
2
10
10
3x9
21. Let f F(x) =
x2
(a) State the domain.
Answer:
(b) State the horizontal asymptote.
Answer:
(c) State the vertical asymptote(s).
Answer:
(d) Which of the following represents the graph of f(x) = 3x9 ? Answer:
GRAPHA.
GRAPH B.
10
10
5.
5
10
5
5
10
10
5
10
5
5
10
10
GRAPH C.
GRAPH D.
10
10
5
5
10
5
5
10
10
5
5
10
5
54
10
10
SHORT ANSWER, with work required to be shown, as indicated.
22. Let f(x)=Vx3 = and g(x) = x  7. 
(a) Find
work.
(b) Find the domain of the quotient function Explain.
g
23. Points (1,8) and (5, 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 yaxis.
24. Find the equation for a line which passes through the points (5,6) and (2,9). Write the
equation in slopeintercept form. Show work.
25. A salesperson earns a base salary of $1,960 per month and a commission of 6.8% on the
amount of sales. If the salesperson has a paycheck of $4,197.20 for one month, what was the
amount of sales for the month? Show work.
26. Let f (x) = 2x2  3 and g(x) = X 4.
(a) Find the composite function (fog 8)(x) and simplify. Show work.
(b) Find (fog)(1). Show work.
27. Find the exact solutions and simplify as much as possible: 5x2 + 6 = 12x. Show work.
28. Given the function f (x) 1 find formula for the inverse function. Show work.
a
29. Donut Delights, Inc. has determined that when x donuts are made daily, the profit P (in
dollars) is given by
P(x)=0.001 x²+3.2x1250 = 
(a) What is the company's profit if 900 donuts are made daily?
(b) How many donuts should be made daily in order to maximize the company's profit? Show
work.
30. Solve: x+7 + 24 = 0. Show work.
x+3
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1. D
2. B
3. A
4. C
5. A...