1. What is the range of ƒ(x) = |x – 3| 2?
A. B. C. D. {x | x ≥ 3}
{y | y ≥ 2}
{x | x ∈ real numbers}
{y | y ∈ real numbers}
2. If f(x) = x2 − 6 for x ≥ 0, find the inverse function, f −1(x).
A. B. C. D. 3. The minimum point on the graph of the equation y = f(x) is (−1,−3). What is the minimum point on the graph of
the equation y = f(x) 5?
A. B. C. D. (−1,2)
(−1,−8)
(4,−3)
(−6,−3)
4. What are the domain and the range of the function shown in the graph below?
A. B. C. D. {x | x > −4}; {y | y > 2}
{x | x ≥ −4}; {y | y ≥ 2}
{x | x > 2}; {y | y > −4}
{x | x ≥ 2}; {y | y ≥ −4}
5. What is the domain of the function: A. B. C. D. ?
(−∞,∞)
(2,∞)
[2,∞)
[3,∞)
6. The height, f(x), of a bouncing ball after x bounces is represented by f(x) = 80(0.5)x. How many times higher is
the first bounce than the fourth bounce?
A. B. C. D. 8
2
16
4
7. If a function is defined by the equation y = 3x 2, which
equation defines the inverse of this function?
12. Given: the function f defined by f(x) = 3x2 − 4. Which
statement is true?
A. B. C. D. A. B. C. f(0) = 0
f(-2) = f(2)
f(5) f(2) = f(7)
f(5) f(2) = f(10)
13. Which equation is the inverse of y = 3x?
D. y = -3x - 2
A. x = 3
B. y = x
8. What is the domain of the function C. y = 3
D. x = ?
y
A. 14. If f(x) = x2 − 3, then f(a − b) is equivalent to
B. C. A. a 2 − b 2 − 3
D. B. a 2 − 2ab − b 2 − 3
C. a 2 − 2ab b 2 − 3
D. a 2 b 2 − 3
9. If f(x) = -2x 7 and g(x) = x2 - 2, then f(g(3)) is equal to
A. B. C. D. -7
-3
-1
7
15. If h(x) = 2x − 1 and g(x) = 3x 1, what is (h g)(2)?
A. B. C. D. 7
10
13
21
10. If f and g are two functions defined by f(x) = 3x 5 and
g(x) = x2 1, then g(f(x)) is
A. x2 3x 6
B. 9x2 30x 26
C. 3x2 8
D. 9x2 26
11. If point (a, b) lies on the graph y = f(x), the graph y =
f -1(x) must contain point
A. B. C. D. (b, a)
(a, 0)
(0, b)
(-a, -b)
16. If A. 4
B. 5
C. 7
D. 13
, find f(8).
17. If f(x) = , what is the value of f(4)?
22. Find the equation for an absolute value function
given the vertex is (-1, 0) and that it also contains the
point (0, 3).
A. 1
A. B. B. 2
C. C. 2
D. D. 4
23. Describe the horizontal and/or the vertical shifts
used to transform the equation y = x2 into the equation y
18. If A. B. C. D. , find f(64).
5
17
65
1025
19. What is the transformation used to transform the
equation into ?
A. B. C. D. T-8, -6
D8, -6
T8, -6
T8, 6
= (x - 1)2 .
A. left 1 unit and down 1 unit
B. left 1 unit, only
C. right 1 unit, only
D. right 1 unit and up 1 unit
24. If f(x) = x2 2, then which expression below represents
f(x h)? A. x2 2xh h 2 2
B. x2 2xh h 2
C. x2 4xh 2
D. x2 2xh 2
25. If g(x) = x2 - 2x, what is g(3x)?
20. What is a possible equation for a parabola whose
range is y ≤ 0 and whose vertex has been shifted to the
left ‘3’, compared to the vertex of the equation y = x2 ?
A. y = (x 3)2
B. y = 3x2 3
C. y = -x2 - 3
D. y = -2(x 3)2
A. 3x2 - 6x
B. 3x2
C. 9x2 - 6x
D. 9x2 - 6
26. If f(x) = 3x2 , then f(x 1) is
A. 3x2 6x 3
21. Which is a possible equation for a parabola that,
compared to the vertex for y = x2 , that has been shifted
down ‘2’ and to the right ‘6’? A. y = 2(x - 6) - 2
B. y = 0.5(x - 6)2 - 2
C. y = -3(x 6)2 - 2
D. y = -(x 6)2 2
B. 3x2 - 6x - 3
C. 3x2 2x 1
D. 3x2 6x - 3
27. Describe the shifts in direction and in quantity of the
vertex when the equation changes to the
equation A. B. C. D. .
right 2 units and up 1 unit
left 2 and up 1 unit
right 1 units and up 2 units
left 1 unit and down 2 units
28. What are the directional changes and numerical
changes of the vertex of the graph of the equation y = x2
when it changes to the equation y = (x - 3)2 5?
A. right 5 units and up 3 units
B. right 3 units and down 5 units
C. right 3 units and up 5 units
D. right 5 units and down 3 units
29. Which ordered pair is in the solution set of the
system of equations shown below?
y2 – x2 32 = 0
3y – x = 0
A. B. C. D. (2, 6)
(3, 1)
(–1, –3)
(–6, –2)
30. Which equation represents the circle shown in the
graph below that passes through the point (0,−1)?
31. Which circle has the smallest circumference?
A. (x – 4)2 y2 = 18
B. (x – 5)2 y2 = 16
C. (x 8)2 (y – 10)2 = 12
D. x2 (y – 1)2 = 10
32. The graph of y = (x - 3)2 is shifted left 4 units and
down 2 units. What is the axis of symmetry of the
transformed graph?
A. B. C. D. x = -2
x = -1
x = 1
x = 7
33. For which quadratic equation is the axis of symmetry
x = 3?
A. y = −x2 3x 5
B. y = −x2 6x 2
C. y = x2 6x 3
D. y = x2 x 3
34. What is the turning point, or vertex, of the parabola
whose equation is y = 3x2 6x− 1?
A. B. C. D. (1, 8)
(−1,−4)
(−3, 8)
(3, 44)
35. The coordinates of the turning point of the graph of
the equation y = x2 − 2x − 8 are (1, k). What is the value
of k?
A. 1 A. (x − 3)2 (y 4)2 = 16
B. 1 − C. 9
D. −9
B. (x − 3)2 (y 4)2 = 18
C. (x 3)2 (y − 4)2 = 16
D. (x 3)2 (y − 4)2 = 18
36. A parabola whose equation is y = x2 − 2x k has a
turning point with coordinates (1, −5). Find the value of
k.
A. B. C. D. −6
−4
0
4
Answer Key for Math 2 Final Exam Review Unit 3 sp2015
1. B 13. B 25. C
2. C 14. C 26. A
3. A
4. B
5. C
6. A
15. C 27. B
16. B 28. C
17. B 29. D
18. B 30. B
7. C 19. C 31. D
8. B 20. D 32. B
9. A 21. B 33. B
10. B 22. A 34. B
11. A 23. C 35. D
12. B 24. A 36. B