Assignment Prompt & Instructions
Please solve equations
**files (1)**
– ## review_problems.pdf
**## review_problems.pdf**
ALGEBRA REVIEW
Name
Student Code
Teaching Assistant
Instructor
1
1. The graph of a function f is given below on the left. After transformation of the graph of f we obtain the
graph g on the right. From the answer choices below select the one which best represents the graph of g.
f g
(a) g(x) = |f(x2 )|
(b) g(x) = −2f(|x|)
(c) g(x) = 4|f(x)|
(d) g(x) = −|2f(x)|
(e) g(x) = −2f(−|x|)
2. Find the solution set for the inequality
−1
6
x ≥ 5
4
+
7
3
x
.
(a) x ∈ [2,+∞)
(b) x ∈ (−∞,−2]
(c) x ∈
(
−∞,−1
2
]
(d) x ∈
[
−1
2
,+∞
)
(e) x ∈ [−2,+∞)
3. logπ(e) = x implies that
(a) eπ = x
(b) ex = π
(c) πx = e
(d) πe = x
(e) xπ = e
2
4. Write the inequality −8 ≤ x < 5 using interval notation.
(a) x ∈ (−8, 5]
(b) x ∈ [−8, 5)
(c) x ∈ (−∞, 5)
(d) x ∈ [−8, 5]
(e) none of the other choices
5. Solve for x:
a
x
= c− b
x
.
(a) c(a+ b)
(b)
ab
c(a+ b)
(c)
a+ b
c
(d) − ab
c(a+ b)
(e)
c
a+ b
6. Find the equation of the line perpendicular to the line y = −4x− 5 containing the point (2, 1).
(a) −x+ 4y = 2
(b) 4x− y = 7
(c) −4x+ y = −7
(d) x− 4y = 2
(e) 4y − x = 3
3
Problems 24-25 refer to the graph below.
7. The function f has codomain (range)
(a) y ∈ (2, 0)
(b) y ∈ [−2, 5]
(c) y ∈ (−2, 3)
(d) y ∈ [−2, 3]
(e) y ∈ (−∞,+∞)
8. The function f is negative on the interval(s)
(a) x ∈ (−4, 2)
(b) x ∈ [−4, 0) ∪ (4, 6)
(c) x ∈ (0, 4)
(d) x ∈ (−∞,+∞)
(e) f is never negative
9. Let f(x) =
√
x. Apply the following sequence of transformations to the graph of f .
(i) Shift down 3 units.
(ii) Reflect about the x-axis
(iii) Shift left 8 units.
Find the function p(x) that represents the resulting graph.
(a) p(x) =
√
x+ 8 + 3
(b) p(x) = −
√
x− 8− 3
(c) p(x) = −
√
x+ 8− 3
(d) p(x) =
√
−x− 8 + 3
(e) p(x) = −
√
x+ 8 + 3
4
10. For the graph of g below, define g piecewise.
(a) g(x) =
3
4x+ 4 if −3 ≤ x ≤ 0
3
2x if 0 < x ≤ 3
(b) g(x) =
4
3x+ 4 if −3 ≤ x ≤ 0
2
3x+ 2 if 0 < x ≤ 3
(c) g(x) =
4
3x+ 4 if −3 ≤ x < 0
2
3x if 0 ≤ x ≤ 3
(d) g(x) =
4
3x− 4 if −3 ≤ x ≤ 0
2
3x if 0 < x ≤ 3
(e) g(x) =
4
3x+ 4 if −3 ≤ x ≤ 0
2
3x if 0 < x ≤ 3
11. Find the equation of the line containing the points (−6, 3) and (8, 8).
(a) y = − 5
14x+ 36
7
(b) y = 5
14x+ 36
7
(c) y + 3 = 5
14x(x+ 6)
(d) y = 14
5 x−
36
7
(e) y = 14
5 x+ 36
7
12. Find the center (h, k) and radius r of the circle (x− 2)2 + (y + 8)2 = 36.
(a) (−8, 2), r = 36
(b) (−2, 8), r = 6
(c) (−8, 2), r = 6
(d) (2,−8), r = 36
(e) (2,−8), r = 6
5
13. The graph of a function f is given below on the left. After transformation of the graph of f we obtain the
graph g on the right. From the answer choices below select the one which best represents the graph of g.
f g
(a) g(x) = f(x− 2)− 1
(b) g(x) = f(x+ 2)− 1
(c) g(x) = f(x− 2) + 1
(d) g(x) = −f(x+ 2)− 1
(e) g(x) = f(x+ 2) + 1
14. Which of the following relations, graphs, or correspondences represents a function?
A. x2 − 5y2 = 1 B. {(−1, 8), (1, 5), (5,−5), (7,−1)}
C. D. xy3 = −6
E. F.
(a) C, B, E (b) B, D,C (c) A, B, C, D, (d) B, D, E (e) A, D, E
6
Questions 32-35 refer to the following function: f(x) = −x2 + 2x+ 5
15. The function f(x) = −x2 + 2x+ 5 opens
(a) upwards
(b) to the left
(c) to the right
(d) downwards
(e) diagonally
16. The vertex of f(x) = −x2 + 2x+ 5 is
(a) (-1,2)
(b) (-2,-3)
(c) (-1,4)
(d) (1,8)
(e) (1,6)
17. The y-intercept of f(x) = −x2 + 2x+ 5 is
(a) (5,0)
(b) (0,-5)
(c) (0,5), (0,-5)
(d) (0,5)
(e) (0,7)
18. The x-intercept(s), in simplified form, of the function f(x) = −x2 + 2x+ 5 is/are
(a)
(
1± 2
√
6, 0
)
(b)
(
− 1±
√
6
)
(c)
(
1±
√
6, 0
)
(d)
(−2±
√
24
2
, 0
)
(e) (1,6)
19. If f(x) is a one to one function with the point (2,−1
3) lying on the graph of f(x), then the inverse function
f−1(x) necessarily has which point lying on it’s graph?
(a) (12 ,−3)
(b) (−3, 12)
(c) (−2, 13)
(d) (−1
3 , 2)
(e) (2,−1
3)
7
20. The function h(x) = (x+ 4)(x+ 2)(x− 2)2 is positive in the interval
(a) x ∈ (−∞,−4)
(b) x ∈ (−∞,−4) ∪ (−2, 2) ∪ (2,+∞)
(c) x ∈ (−∞,+∞)
(d) x ∈ (−4,−2)
(e) (-3,2)
21. Find the quadratic function with graph given below.
(a) f(x) = −1
4(x− 2)2 + 3
(b) f(x) = −(x− 2)2 + 3
(c) f(x) = (x+ 2)2 − 3
(d) f(x) = 4(x+ 2)2 − 3
(e) f(x) = 1
4(x− 2)2 − 3
22. For the given functions f(x) = 2x and g(x) = 3×2 + 1, find (g ◦ f)(−2).
(a) 26
(b) -52
(c) 25
(d) 49
(e) 56
Questions 40-44 refer to the graph of the function g(x) = − log5(−x+ 2).
23. The codomain (range) of the function g(x) consists of all
(a) y ∈ (−2,+∞)
(b) y ∈ (−∞,+∞)
(c) y ∈ (−∞,−2)
(d) y ∈ [0,+∞)
(e) y ∈ (−∞,−2]
8
For problem 41, select the choice that best describes the properties of the graph of g(x).
24. The function g(x) has asymptote given by the line .
(a) vertical, x = −2
(b) horizontal, y = 0
(c) vertical x = 0
(d) horizontal, y = 2
(e) vertical, x = 2
25. The function g(x) has x-intercept
(a) (1, 0)
(b) (2, 0)
(c) (5, 0)
(d) (0, 0)
(e) g has no x-intercept
26. The function g(x) is increasing on the interval
(a) x ∈ (2,+∞)
(b) x ∈ (−∞,+∞)
(c) x ∈ (−∞, 2)
(d) x ∈ [2,+∞)
(e) g is never increasing
27. The function g(x) has inverse function
(a) g−1(x) = 5−x − 2
(b) g−1(x) = 5−x−2
(c) g−1(x) = −5−x + 2
(d) g−1(x) =
1
− log5(−x+ 2)
(e) g−1(x) = − log5(2− x)
28. The circle above has center
(a) (−3, 2) (b) (3, 2) (c) (32 , 2) (d) (52 , 2) (e) (2, 52)
9
29. ln(y) = 2 ln(x)− ln(x+ 1)− ln(C) implies that
(a) y = −Cx2(x+ 1)
(b) y =
C(x+ 1)
x2
(c) y =
x2
C(x+ 1)
(d) y = ln(Cx)
(e)
x+ 1
Cx2
30. If 5x = 2 what is 53x?
(a)2
(b)4
(c)8
(d)16
(e)32
31. Solve log4 (x− 1) = 2 for x
(a) x = 17
(b) x = 8
(c) x = 2, x = −9
(d) x = 9
(e) x = −2
32. The x-intercept of f(x) = 30− 12ex is
(a) (e
√
2, 0)
(b) (ln(
5
2
), 0)
(c) (40, 0)
(d) (60, 0)
(e) (
ln(30)
ln(12)
, 0)
10
Problems 50-51 refer to the graph below.
33. The function f is strictly increasing on the interval(s)
(a) x ∈ −2, 4)
(b) x ∈ (3, 6)
(c) x ∈ (−6,−4)
(d) x ∈ (−4, 0)
(e) f is never increasing
34. The function f is constant on the interval(s)
(a) x ∈ (0, 3)
(b) x ∈ (−4, 0)
(c) x ∈ (−6,−4)
(d) x ∈ [3, 6]
(e) f is never constant
35. Solve the system of equations
−x+ 2y = 7
3x− 5y = 2
(a) (39, 23)
(b) (2,−2)
(c) (4, 1)
(d) (−39, 23)
(e) (24, 16)
11
36. Which graph best represents the graph of f(x) = −3x + 1?
graph 1 graph 2
graph 3 graph 4
graph 5 graph 6
(a) graph 3
(b) graph 2
(c) graph 1
(d) graph 6
(e) graph 5
12
37. Which of the following graphs best represents the solution the system of equations
xy = −4
x2 + y2 = 8
A. B.
C. D.
(a) A
(b) B
(c) C
(d) D
(e) none of the other choices
13
38. Which graph best represents the graph of f(x) = log3(−x+ 1)?
graph 1 graph 2
graph 3 graph 4
graph 5 graph 6
(a) graph 3
(b) graph 2
(c) graph 1
(d) graph 6
(e) graph 5
39. Find the quadratic function with graph given below.
14
(a) f(x) = −(x− 2)2 + 3
(b) f(x) = −1
4(x− 2)2 + 3
(c) f(x) = 1
4(x− 2)2 − 3
(d) f(x) = (x+ 2)2 − 3
(e) f(x) = 4(x+ 2)2 − 3
Questions 2-5 refer to the function h(x) = −x2(x2 − 81)(x+ 9)
40. The function h(x) is negative in the interval
(a) x ∈ (−∞,−9)
(b) x ∈ (9,+∞)
(c) x ∈ (−∞,+∞)
(d) x ∈ (−∞,−9) ∪ (−9, 0) ∪ (0, 9)
(e) h is never negative
41. The function h(x) is positive in the interval
(a) x ∈ (−∞,−9)
(b) x ∈ (9,+∞)
(c) x ∈ (−∞,+∞)
(d) x ∈ (−∞,−9) ∪ (−9, 0) ∪ (0, 9)
(e) h is never positive
42. Which of the following best describes the end behaviour of h(x)
(a) as x→ −∞, h(x)→ +∞ and as x→ +∞, h(x)→ −∞
(b) as x→ −∞, h(x)→ −∞ and as x→ +∞, h(x)→ +∞
(c) as x→ −∞, h(x)→ −∞ and as x→ +∞, h(x)→ −∞
(d) as x→ −∞, h(x)→ +∞ and as x→ +∞, h(x)→ +∞
(e) none of the other choices
43. Which graph best represents the graph of h(x)?
15
graph 1 graph 2
graph 3 graph 4
(a) graph 1
(b) graph 2
(c) graph 3
(d) graph 4
(e) none of the other choices
16
44. Let f(x) =
3
x+ 2
. Then for x 6= 1,
f(x)− f(1)
x− 1
=
(a)
3
x(x+ 2)
(b)
1
x+ 2
(c)
3
(x− 1)(x+ 2)
(d)
−1
x+ 2
(e)
−x+ 5
x− 1
45. Let f(x) = 7x+ 4. Then for h 6= 0,
f(x+ h)− f(x)
h
=
(a) 7 +
14(x+ 4)
h
(b) 0
(c) 7
(d) 7 +
8
h
(e)
h+ 8
h
46. Let f(x) =
√
2x and a = 2. Geometrically, the difference quotient
f(x)− f(a)
x− a
is equal to
(a) the slope of the secant line passing through the point (x,
√
2x)) and the point (2, 2)
(b) the slope of the tangent line passing through the point (x, f(x)) and the point (2,
√
2)
(c) the slope of the secant line passing through the point (−x, f(x)) and the point (2, 2)
(d) the average height of the function between the point (x, f(x)) and the point (2,
√
2)
(e) the slope of the secant line passing through the point (−x,
√
2x)) and the point (2, 2)
17
Questions 9-17 refer to the function f(x) =
−x+ 1 if −1 ≤ x < 1
2 if x = 1
x2 if x > 1
47. The domain of f(x) consists of all
(a) x ∈ (−∞,+∞)
(b) x ∈ (−1, 1)
(c) x ∈ [−1, 1]
(d) x ∈ [−1,∞)
(e) none of the above
48. The range of f(x) consists of all
(a) y ∈ (−∞,+∞)
(b) y ∈ [0,∞)
(c) y ∈ (0,∞]
(d) y ∈ (−1, 1)
(e) none of the above
49. The function f(x) is increasing on the interval
(a) x ∈ (−∞,∞)
(b) x ∈ (1,∞)
(c) x ∈ (−∞, 1)
(d) x ∈ (−1, 1)
(e) none of the above
50. The function f(x) is decreasing on the interval
(a) x ∈ (−∞,∞)
(b) x ∈ (1,∞)
(c) x ∈ (−∞, 1)
(e) x ∈ (−1, 1)
(e) none of the above
18
51. As x→ +∞, f(x)→ ?
(a) f(x)→ +∞
(b) f(x)→ −∞
(c) f(x)→ 2
(d) f(x)→ −2
(e) f(x)→ 0
52. The function f(x) has x-intercept(s)
(a) (1, 0)
(b) (−1, 0), (1, 0)
(c) (0, 0)
(d) (−1, 0)
(e) none
53. The function f(x) has y-intercept(s)
(a) (0, 1)
(b) (0,−1), (0, 1)
(c) (0, 0)
(d) (0,−1)
(e) none
54. The function f(x) is negative in the interval
(a) x ∈ (−∞,+∞)
(b) x ∈ (−1, 1)
(c) x ∈ (1,∞)
(d) x ∈ (−∞, 1)
(e) never
19
55. The function f(x) is positive in the interval
(a) x ∈ (−∞,+∞)
(b) x ∈ (−1, 1)
(c) x ∈ (1,∞)
(d) x ∈ [−1,∞)
(e) never
56. f(34)
(a) 1
4 , 2, 9
16
(b) 2
(c) 9
4
(d) 1
4
(e) 9
16
57. A projectile is thrown upward so that its distance above the ground after t seconds is h(t) = −10t2 + 280t.
After how many seconds does it reach its maximum height?
(a) 7 sec
(b) 14 sec
(c) 21 sec
(d) 28 sec
(e) 35 sec
58. You have 120 feet of fencing to enclose a rectangular plot that borders a river. If you do not fence the side
along the river, find the length and width of the plot that will maximize the area.
(a) length: 60 ft, width: 30 ft
(b) length: 90 ft, width: 30 ft
(c) length: 60 ft, width: 60 ft
(d) length: 30 ft, width: 30 ft
(e) none of the above
20
59. The price p (in dollars) and the quantity x sold of a certain product obey the demand equation x = −5p+100, 0 ≤
p ≤ 20. Express the revenue R as a function of x. and find the value of x that maximizes revenue (xmax).
(a) R(x) = p(−5p+ 100), xmax = 25
4
(b) R(x) = x(−5x+ 100), xmax = 100
5
(c) R(x) = x
(
x− 100
5
)
, xmax = 50
2
(d) R(x) = x
(
x− 100
−5
)
, xmax = 100
2
(e) none of the above
60. Find the vertex and axis of symmetry for f(x) = −x2 + 12x+ 4
(a) (12, 4); x = 12
(b) (−6,−32); x = −6
(c) (−6,−104); x = −6
(d) (6, 40); x = 6
(e) (6, 40); x = 40
61. Determine the domain and range of f(x) = x2 − 4x+ 4
(a) Domain: (−∞,+∞), Range: [4,+∞)
(b) Domain: (−∞,+∞), Range: [0,+∞)
(c) Domain: (−2,+∞), Range: [0,+∞)
(d) Domain: (2,+∞), Range: [0,+∞)
(e) Domain: (−∞,+∞), Range: [16,+∞)
62. For the function: f(x) =
{
x− 1 if −3 < x < 0
3x− 1 if x ≥ 0
Find f(−3).
(a) − 4
(b) Undefined
(c) − 10
(d) − 2
(e) none of the above
63. For the polynomial f(x) = 2(x+ 5)(x− 6)4 list each real zero and its multiplicity.
(a) − 5,multiplicity 1; 6 multiplicity 4
(b) 5 multiplicity 1; −6 multiplicity 4
(c) − 5 multiplicity 1; 6, multiplicity 4
(d) 5 multiplicity 1; −6, multiplicity 4
(e) 2,multiplicity 1, −5 multiplicity 1; 6, multiplicity 4
21
64. Which of the following polynomial functions could have the graph given below?
(A) y = −(x− 4)(x− 2)(x+ 2)
(B) y = (x2 + 1
2)(x2 − 4)(4− x)
(C) y = −1
2
(x2 − 4)2(x− 4)
(D) y = (x2 − 4)(1− x
4
)
(E) y = −1
2
(x2 + 4)(x− 4)
(F) y =
1
2
(x2 − 4)2(x− 4)
(a) F only
(b) B, D, and A
(c) C,E, and F
(d) B and D only
(e) A only
22
**## review_problems.pdf**
ALGEBRA REVIEW
Name
Student Code
Teaching Assistant
Instructor
1
1. The graph of a function f is given below on the left. After transformation of the graph of f we obtain the
graph g on the right. From the answer choices below select the one which best represents the graph of g.
f g
(a) g(x) = |f(x2 )|
(b) g(x) = −2f(|x|)
(c) g(x) = 4|f(x)|
(d) g(x) = −|2f(x)|
(e) g(x) = −2f(−|x|)
2. Find the solution set for the inequality
−1
6
x ≥ 5
4
+
7
3
x
.
(a) x ∈ [2,+∞)
(b) x ∈ (−∞,−2]
(c) x ∈
(
−∞,−1
2
]
(d) x ∈
[
−1
2
,+∞
)
(e) x ∈ [−2,+∞)
3. logπ(e) = x implies that
(a) eπ = x
(b) ex = π
(c) πx = e
(d) πe = x
(e) xπ = e
2
4. Write the inequality −8 ≤ x < 5 using interval notation.
(a) x ∈ (−8, 5]
(b) x ∈ [−8, 5)
(c) x ∈ (−∞, 5)
(d) x ∈ [−8, 5]
(e) none of the other choices
5. Solve for x:
a
x
= c− b
x
.
(a) c(a+ b)
(b)
ab
c(a+ b)
(c)
a+ b
c
(d) − ab
c(a+ b)
(e)
c
a+ b
6. Find the equation of the line perpendicular to the line y = −4x− 5 containing the point (2, 1).
(a) −x+ 4y = 2
(b) 4x− y = 7
(c) −4x+ y = −7
(d) x− 4y = 2
(e) 4y − x = 3
3
Problems 24-25 refer to the graph below.
7. The function f has codomain (range)
(a) y ∈ (2, 0)
(b) y ∈ [−2, 5]
(c) y ∈ (−2, 3)
(d) y ∈ [−2, 3]
(e) y ∈ (−∞,+∞)
8. The function f is negative on the interval(s)
(a) x ∈ (−4, 2)
(b) x ∈ [−4, 0) ∪ (4, 6)
(c) x ∈ (0, 4)
(d) x ∈ (−∞,+∞)
(e) f is never negative
9. Let f(x) =
√
x. Apply the following sequence of transformations to the graph of f .
(i) Shift down 3 units.
(ii) Reflect about the x-axis
(iii) Shift left 8 units.
Find the function p(x) that represents the resulting graph.
(a) p(x) =
√
x+ 8 + 3
(b) p(x) = −
√
x− 8− 3
(c) p(x) = −
√
x+ 8− 3
(d) p(x) =
√
−x− 8 + 3
(e) p(x) = −
√
x+ 8 + 3
4
10. For the graph of g below, define g piecewise.
(a) g(x) =
3
4x+ 4 if −3 ≤ x ≤ 0
3
2x if 0 < x ≤ 3
(b) g(x) =
4
3x+ 4 if −3 ≤ x ≤ 0
2
3x+ 2 if 0 < x ≤ 3
(c) g(x) =
4
3x+ 4 if −3 ≤ x < 0
2
3x if 0 ≤ x ≤ 3
(d) g(x) =
4
3x− 4 if −3 ≤ x ≤ 0
2
3x if 0 < x ≤ 3
(e) g(x) =
4
3x+ 4 if −3 ≤ x ≤ 0
2
3x if 0 < x ≤ 3
11. Find the equation of the line containing the points (−6, 3) and (8, 8).
(a) y = − 5
14x+ 36
7
(b) y = 5
14x+ 36
7
(c) y + 3 = 5
14x(x+ 6)
(d) y = 14
5 x−
36
7
(e) y = 14
5 x+ 36
7
12. Find the center (h, k) and radius r of the circle (x− 2)2 + (y + 8)2 = 36.
(a) (−8, 2), r = 36
(b) (−2, 8), r = 6
(c) (−8, 2), r = 6
(d) (2,−8), r = 36
(e) (2,−8), r = 6
5
13. The graph of a function f is given below on the left. After transformation of the graph of f we obtain the
graph g on the right. From the answer choices below select the one which best represents the graph of g.
f g
(a) g(x) = f(x− 2)− 1
(b) g(x) = f(x+ 2)− 1
(c) g(x) = f(x− 2) + 1
(d) g(x) = −f(x+ 2)− 1
(e) g(x) = f(x+ 2) + 1
14. Which of the following relations, graphs, or correspondences represents a function?
A. x2 − 5y2 = 1 B. {(−1, 8), (1, 5), (5,−5), (7,−1)}
C. D. xy3 = −6
E. F.
(a) C, B, E (b) B, D,C (c) A, B, C, D, (d) B, D, E (e) A, D, E
6
Questions 32-35 refer to the following function: f(x) = −x2 + 2x+ 5
15. The function f(x) = −x2 + 2x+ 5 opens
(a) upwards
(b) to the left
(c) to the right
(d) downwards
(e) diagonally
16. The vertex of f(x) = −x2 + 2x+ 5 is
(a) (-1,2)
(b) (-2,-3)
(c) (-1,4)
(d) (1,8)
(e) (1,6)
17. The y-intercept of f(x) = −x2 + 2x+ 5 is
(a) (5,0)
(b) (0,-5)
(c) (0,5), (0,-5)
(d) (0,5)
(e) (0,7)
18. The x-intercept(s), in simplified form, of the function f(x) = −x2 + 2x+ 5 is/are
(a)
(
1± 2
√
6, 0
)
(b)
(
− 1±
√
6
)
(c)
(
1±
√
6, 0
)
(d)
(−2±
√
24
2
, 0
)
(e) (1,6)
19. If f(x) is a one to one function with the point (2,−1
3) lying on the graph of f(x), then the inverse function
f−1(x) necessarily has which point lying on it’s graph?
(a) (12 ,−3)
(b) (−3, 12)
(c) (−2, 13)
(d) (−1
3 , 2)
(e) (2,−1
3)
7
20. The function h(x) = (x+ 4)(x+ 2)(x− 2)2 is positive in the interval
(a) x ∈ (−∞,−4)
(b) x ∈ (−∞,−4) ∪ (−2, 2) ∪ (2,+∞)
(c) x ∈ (−∞,+∞)
(d) x ∈ (−4,−2)
(e) (-3,2)
21. Find the quadratic function with graph given below.
(a) f(x) = −1
4(x− 2)2 + 3
(b) f(x) = −(x− 2)2 + 3
(c) f(x) = (x+ 2)2 − 3
(d) f(x) = 4(x+ 2)2 − 3
(e) f(x) = 1
4(x− 2)2 − 3
22. For the given functions f(x) = 2x and g(x) = 3×2 + 1, find (g ◦ f)(−2).
(a) 26
(b) -52
(c) 25
(d) 49
(e) 56
Questions 40-44 refer to the graph of the function g(x) = − log5(−x+ 2).
23. The codomain (range) of the function g(x) consists of all
(a) y ∈ (−2,+∞)
(b) y ∈ (−∞,+∞)
(c) y ∈ (−∞,−2)
(d) y ∈ [0,+∞)
(e) y ∈ (−∞,−2]
8
For problem 41, select the choice that best describes the properties of the graph of g(x).
24. The function g(x) has asymptote given by the line .
(a) vertical, x = −2
(b) horizontal, y = 0
(c) vertical x = 0
(d) horizontal, y = 2
(e) vertical, x = 2
25. The function g(x) has x-intercept
(a) (1, 0)
(b) (2, 0)
(c) (5, 0)
(d) (0, 0)
(e) g has no x-intercept
26. The function g(x) is increasing on the interval
(a) x ∈ (2,+∞)
(b) x ∈ (−∞,+∞)
(c) x ∈ (−∞, 2)
(d) x ∈ [2,+∞)
(e) g is never increasing
27. The function g(x) has inverse function
(a) g−1(x) = 5−x − 2
(b) g−1(x) = 5−x−2
(c) g−1(x) = −5−x + 2
(d) g−1(x) =
1
− log5(−x+ 2)
(e) g−1(x) = − log5(2− x)
28. The circle above has center
(a) (−3, 2) (b) (3, 2) (c) (32 , 2) (d) (52 , 2) (e) (2, 52)
9
29. ln(y) = 2 ln(x)− ln(x+ 1)− ln(C) implies that
(a) y = −Cx2(x+ 1)
(b) y =
C(x+ 1)
x2
(c) y =
x2
C(x+ 1)
(d) y = ln(Cx)
(e)
x+ 1
Cx2
30. If 5x = 2 what is 53x?
(a)2
(b)4
(c)8
(d)16
(e)32
31. Solve log4 (x− 1) = 2 for x
(a) x = 17
(b) x = 8
(c) x = 2, x = −9
(d) x = 9
(e) x = −2
32. The x-intercept of f(x) = 30− 12ex is
(a) (e
√
2, 0)
(b) (ln(
5
2
), 0)
(c) (40, 0)
(d) (60, 0)
(e) (
ln(30)
ln(12)
, 0)
10
Problems 50-51 refer to the graph below.
33. The function f is strictly increasing on the interval(s)
(a) x ∈ −2, 4)
(b) x ∈ (3, 6)
(c) x ∈ (−6,−4)
(d) x ∈ (−4, 0)
(e) f is never increasing
34. The function f is constant on the interval(s)
(a) x ∈ (0, 3)
(b) x ∈ (−4, 0)
(c) x ∈ (−6,−4)
(d) x ∈ [3, 6]
(e) f is never constant
35. Solve the system of equations
−x+ 2y = 7
3x− 5y = 2
(a) (39, 23)
(b) (2,−2)
(c) (4, 1)
(d) (−39, 23)
(e) (24, 16)
11
36. Which graph best represents the graph of f(x) = −3x + 1?
graph 1 graph 2
graph 3 graph 4
graph 5 graph 6
(a) graph 3
(b) graph 2
(c) graph 1
(d) graph 6
(e) graph 5
12
37. Which of the following graphs best represents the solution the system of equations
xy = −4
x2 + y2 = 8
A. B.
C. D.
(a) A
(b) B
(c) C
(d) D
(e) none of the other choices
13
38. Which graph best represents the graph of f(x) = log3(−x+ 1)?
graph 1 graph 2
graph 3 graph 4
graph 5 graph 6
(a) graph 3
(b) graph 2
(c) graph 1
(d) graph 6
(e) graph 5
39. Find the quadratic function with graph given below.
14
(a) f(x) = −(x− 2)2 + 3
(b) f(x) = −1
4(x− 2)2 + 3
(c) f(x) = 1
4(x− 2)2 − 3
(d) f(x) = (x+ 2)2 − 3
(e) f(x) = 4(x+ 2)2 − 3
Questions 2-5 refer to the function h(x) = −x2(x2 − 81)(x+ 9)
40. The function h(x) is negative in the interval
(a) x ∈ (−∞,−9)
(b) x ∈ (9,+∞)
(c) x ∈ (−∞,+∞)
(d) x ∈ (−∞,−9) ∪ (−9, 0) ∪ (0, 9)
(e) h is never negative
41. The function h(x) is positive in the interval
(a) x ∈ (−∞,−9)
(b) x ∈ (9,+∞)
(c) x ∈ (−∞,+∞)
(d) x ∈ (−∞,−9) ∪ (−9, 0) ∪ (0, 9)
(e) h is never positive
42. Which of the following best describes the end behaviour of h(x)
(a) as x→ −∞, h(x)→ +∞ and as x→ +∞, h(x)→ −∞
(b) as x→ −∞, h(x)→ −∞ and as x→ +∞, h(x)→ +∞
(c) as x→ −∞, h(x)→ −∞ and as x→ +∞, h(x)→ −∞
(d) as x→ −∞, h(x)→ +∞ and as x→ +∞, h(x)→ +∞
(e) none of the other choices
43. Which graph best represents the graph of h(x)?
15
graph 1 graph 2
graph 3 graph 4
(a) graph 1
(b) graph 2
(c) graph 3
(d) graph 4
(e) none of the other choices
16
44. Let f(x) =
3
x+ 2
. Then for x 6= 1,
f(x)− f(1)
x− 1
=
(a)
3
x(x+ 2)
(b)
1
x+ 2
(c)
3
(x− 1)(x+ 2)
(d)
−1
x+ 2
(e)
−x+ 5
x− 1
45. Let f(x) = 7x+ 4. Then for h 6= 0,
f(x+ h)− f(x)
h
=
(a) 7 +
14(x+ 4)
h
(b) 0
(c) 7
(d) 7 +
8
h
(e)
h+ 8
h
46. Let f(x) =
√
2x and a = 2. Geometrically, the difference quotient
f(x)− f(a)
x− a
is equal to
(a) the slope of the secant line passing through the point (x,
√
2x)) and the point (2, 2)
(b) the slope of the tangent line passing through the point (x, f(x)) and the point (2,
√
2)
(c) the slope of the secant line passing through the point (−x, f(x)) and the point (2, 2)
(d) the average height of the function between the point (x, f(x)) and the point (2,
√
2)
(e) the slope of the secant line passing through the point (−x,
√
2x)) and the point (2, 2)
17
Questions 9-17 refer to the function f(x) =
−x+ 1 if −1 ≤ x < 1
2 if x = 1
x2 if x > 1
47. The domain of f(x) consists of all
(a) x ∈ (−∞,+∞)
(b) x ∈ (−1, 1)
(c) x ∈ [−1, 1]
(d) x ∈ [−1,∞)
(e) none of the above
48. The range of f(x) consists of all
(a) y ∈ (−∞,+∞)
(b) y ∈ [0,∞)
(c) y ∈ (0,∞]
(d) y ∈ (−1, 1)
(e) none of the above
49. The function f(x) is increasing on the interval
(a) x ∈ (−∞,∞)
(b) x ∈ (1,∞)
(c) x ∈ (−∞, 1)
(d) x ∈ (−1, 1)
(e) none of the above
50. The function f(x) is decreasing on the interval
(a) x ∈ (−∞,∞)
(b) x ∈ (1,∞)
(c) x ∈ (−∞, 1)
(e) x ∈ (−1, 1)
(e) none of the above
18
51. As x→ +∞, f(x)→ ?
(a) f(x)→ +∞
(b) f(x)→ −∞
(c) f(x)→ 2
(d) f(x)→ −2
(e) f(x)→ 0
52. The function f(x) has x-intercept(s)
(a) (1, 0)
(b) (−1, 0), (1, 0)
(c) (0, 0)
(d) (−1, 0)
(e) none
53. The function f(x) has y-intercept(s)
(a) (0, 1)
(b) (0,−1), (0, 1)
(c) (0, 0)
(d) (0,−1)
(e) none
54. The function f(x) is negative in the interval
(a) x ∈ (−∞,+∞)
(b) x ∈ (−1, 1)
(c) x ∈ (1,∞)
(d) x ∈ (−∞, 1)
(e) never
19
55. The function f(x) is positive in the interval
(a) x ∈ (−∞,+∞)
(b) x ∈ (−1, 1)
(c) x ∈ (1,∞)
(d) x ∈ [−1,∞)
(e) never
56. f(34)
(a) 1
4 , 2, 9
16
(b) 2
(c) 9
4
(d) 1
4
(e) 9
16
57. A projectile is thrown upward so that its distance above the ground after t seconds is h(t) = −10t2 + 280t.
After how many seconds does it reach its maximum height?
(a) 7 sec
(b) 14 sec
(c) 21 sec
(d) 28 sec
(e) 35 sec
58. You have 120 feet of fencing to enclose a rectangular plot that borders a river. If you do not fence the side
along the river, find the length and width of the plot that will maximize the area.
(a) length: 60 ft, width: 30 ft
(b) length: 90 ft, width: 30 ft
(c) length: 60 ft, width: 60 ft
(d) length: 30 ft, width: 30 ft
(e) none of the above
20
59. The price p (in dollars) and the quantity x sold of a certain product obey the demand equation x = −5p+100, 0 ≤
p ≤ 20. Express the revenue R as a function of x. and find the value of x that maximizes revenue (xmax).
(a) R(x) = p(−5p+ 100), xmax = 25
4
(b) R(x) = x(−5x+ 100), xmax = 100
5
(c) R(x) = x
(
x− 100
5
)
, xmax = 50
2
(d) R(x) = x
(
x− 100
−5
)
, xmax = 100
2
(e) none of the above
60. Find the vertex and axis of symmetry for f(x) = −x2 + 12x+ 4
(a) (12, 4); x = 12
(b) (−6,−32); x = −6
(c) (−6,−104); x = −6
(d) (6, 40); x = 6
(e) (6, 40); x = 40
61. Determine the domain and range of f(x) = x2 − 4x+ 4
(a) Domain: (−∞,+∞), Range: [4,+∞)
(b) Domain: (−∞,+∞), Range: [0,+∞)
(c) Domain: (−2,+∞), Range: [0,+∞)
(d) Domain: (2,+∞), Range: [0,+∞)
(e) Domain: (−∞,+∞), Range: [16,+∞)
62. For the function: f(x) =
{
x− 1 if −3 < x < 0
3x− 1 if x ≥ 0
Find f(−3).
(a) − 4
(b) Undefined
(c) − 10
(d) − 2
(e) none of the above
63. For the polynomial f(x) = 2(x+ 5)(x− 6)4 list each real zero and its multiplicity.
(a) − 5,multiplicity 1; 6 multiplicity 4
(b) 5 multiplicity 1; −6 multiplicity 4
(c) − 5 multiplicity 1; 6, multiplicity 4
(d) 5 multiplicity 1; −6, multiplicity 4
(e) 2,multiplicity 1, −5 multiplicity 1; 6, multiplicity 4
21
64. Which of the following polynomial functions could have the graph given below?
(A) y = −(x− 4)(x− 2)(x+ 2)
(B) y = (x2 + 1
2)(x2 − 4)(4− x)
(C) y = −1
2
(x2 − 4)2(x− 4)
(D) y = (x2 − 4)(1− x
4
)
(E) y = −1
2
(x2 + 4)(x− 4)
(F) y =
1
2
(x2 − 4)2(x− 4)
(a) F only
(b) B, D, and A
(c) C,E, and F
(d) B and D only
(e) A only
22