Transcribed Text

1. Determine the domain and range of the piecewise function.
4 4
4
A. Domain [2, 4]; Range [3, 3]
B. Domain [2, 1]; Range [2, 4]
C. Domain [3, 3]; Range [2, 4]
D. Domain [3, 0]; Range [O, 4]
2. Solve: J276x = x
A. 9
B. 9, 3
C. 27/5
D. No solution
2. __ _
3. Determine the interval(s) on which the function is increasing. 3. __ _
A. (1, 4) Pa.
B. {00,l) and { 4,oo )
4
C. (1/3, 3)and (4.75,oo)
D. (1.25, 3.25)
2 2 .. l:i
4. Determine whether the graph of y = 5 + lxl is symmetric with respect to the origin,
the xaxis, or the yaxis. 4. __ _
A. symmetric with respect to the origin only
B. symmetric with respect to the xaxis only
C. symmetric with respect to the yaxis only
D. not symmetric with respect to the xaxis, not symmetric with respect to the yaxis, and
not symmetric with respect to the origin
5. Solve, and express the answer in interval notation: I 8  6x I 2.
A. (=, 5/3] u [l, =)
B. (=, 1] u [5/3, oo)
C. [1, 5/3]
D. [l, oo)
5. __ _
6. Which of the following represents the graph of 4x  9y == 36 ? 6. __ _
A. B.
10
10
10
10 10
C. D.
10
\
10
5
10
10
7. Write a slopeintercept equation for a line parallel to the line x  Sy= 2 which passes through
the point (15, 2). 7. __ _
A.
1
y=x+l
5
B.
1
y=x5
5
C.
1
y=x2
5
D. y =5x+73
8. Which of the following best describes the graph?
2
2
A. It is the graph of an absolute value relation.
B. It is not the graph of a function.
C. It is a function and it is onetoone.
D. It is a function but not onetoone.
8. __ _
9. Express as an equivalent expression: 8 log (x  3) + log 1  logy
A. Iog(Sx23y)
B.
log(x3)8
log(y)
C.
((x3)')
log
D. log( 8x
24
)
10. Which of the functions corresponds to the graph?
10
8
t3
2
2 2 4 6
A. f (x) =ex +3
B. f (x)=ex +4
C. J(x)=ex +4
D. f(x)=ex+3
9. __ _
10. __
11. A candidate's share of the votes varies direct! y as the number of votes cast for the candidate.
In a city council election with four candidates, Clark received 1,024 votes and earned a 32%
share of the votes. Duncan received 1,440 votes. What was Duncan's corresponding share of the
votes?
11.
A. 45%
B. 58%
C. 68%
D. 74%
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) andf(x)?
4 2
4
2 4 4 2 2
2 2
4 4
y = f (x) y = g(x)
A. g(x) = f (x  2)  1
B. g(x) = f(x + 2)  1
C. g(x) = f(x + 1)  2
D. g(x) = J(x  1)  2
12. __ _
4
SHORT ANSWER:
13W. Mriutelt itphley a annsdw seirm inp ltihfye: fo(8r m 5ai+)( 7 bi,  w2ih).e re a and b are real numbers.
14. Solve, and write the answer in interval notation: x+ 5 0. x+2
Answer:
Answer:
15. A can of soda at 78° 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(t) = 35 + 43e  o.osg 1
Find the temperature of the soda 12 minutes after it is placed in the refrigerator. (Round to the
nearest degree.)
16. Find the value of the logarithm: log7 ( 9) .
17. Solve: 4 7 x 1 = 16 .
Answer: ___ _
Answer: ___ _
Answer: ____
c18on. tSinuupopuossley $. 8H,0ow00 l oisn ign v(teos ttehde inne aanre satc cteonutnht oaft aa ny eaanrn)u wali liln itte traekste rtahtee ionfv 3e.s9tm%e cnot mtop doouunbdleed i n size? Answer: ___ _
19. Letf (x) = x2 + 12x + 28.
(a) Find the vertex.
(b) State the range of the function.
(c) On what interval is the function decreasing?
Answer: ___ _
Answer: __ _
Answer: ___ _
20. Consider the polynomial P(x), shown in both standard form and factored form.
1 4 1 3 7 2 1 1
P(x)=x +x x x+3=(x+3)(x+l)(xl)(x2)
2 2 2 2 2
(a) Which sketch illustrates the end behavior of the polynomial function?
(b) State the zeros of the function.
(c) State theyintercept.
(d) State which graph below is the graph of P(x).
GRAPH A
' ,
10 10
I
,
1 i
GRAPHC
n
f l
:i:T
\1 /\
I I I I I ' I I I I I I ,{. I I I I I I I
10
'
! 5 10
,·
\ I I \
l; e I ,
1, I I  \,I
Answer:
Answer:
GRAPHB
1C,
I ·1
GRAPHD
i
\ i \
\
10 "= \,
I I
\)
1..
Answer: ___ _
Answer:
f
I
10
j
10
Page 8 of 11
3x2 3 21. Let f(x)=2

X 4
(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) = 3
2 3 ? Answer: ______ _
x 4
GRAPH A.
I
•10
GRAPHC.
I I I I f I I
•10 .
.. ...,
,,\
\
\
I
10
.,
11 I l f ; i l
\\ =Tf : / \ l .r
\..!
I i I
_j
j
I
GRAPHB.
GRAPHD.
10
I I I I I I I I I
10
. _ ,...........
/,.
I
I
10
11)
10
l \
:: '"
•:
10
I
I
I
J
10
10
Page 9 of LJ
SHORT ANSWER, with work required to be shown, as indicated.
23. Points (2, 1) and (6, 9) 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 of the circle?
(c) What is the equation of the circle?
24. Find the equation for a line which passes through the points (9, 5) and (7, 3). Write the
equation in slopeintercept form. Show work.
25. Theo, a resident of Metropolis, pays Metropolis an annual tax of $85 plus 1.3% of his annual
income. If Theo paid $1,086 in tax, what was Theo's income? Show work.
26.Letf(x)=7x2 +5 and g(x)=x2.
(a) Find the composite function (fog )(x) and simplify. Show work.
(b) Find (f O g) (1). Show work.
27. Find the exact solutions and simplify as much as possible: 32x2
+ 13 = 40x. Show work.
28. Given the function f (x) = ! x 7, find a formula for the inverse function. Show work. 2
Page 10 of 11
29. The fuel efficiency F for a particular car is given by
F(x) = 0.02 x2 + 1.56 x + 9.8
where xis the speed of the car in miles per hour (mph) and F(x) is the corresponding fuel
efficiency in miles per gallon (mpg).
(a) What is the fuel efficiency if the car's speed is 80 mph?
(b) What speed will yield the maximum fuel efficiency? Show work.
x1 24
30. Solve:  = 2
 . Show work.
x+3 X 9
Page 11 of 11
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Unethical use is strictly forbidden.
1. Correct answer is C
2. Correct answer is A
3. Correct answer is B
4. Correct answer is C
5. Correct answer is B...