AnswersTX-Algebra II BUnit Test

The Cubing Function Answers

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1
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Which statements correctly describe the graph of the function f(x) = x3 – 4x2 – 3x + 18? Select three options.

A
There are three unique solutions to the function when y=0.
B
The function has a double root.
C
As x increases from negative infinity to positive infinity, the y-values increase, decrease, and then increase again.
D
As x approaches negative infinity, y approaches positive infinity.
E
The domain and range of the function are the set of real numbers.
2
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The graph of the parent function f(x) = x3 is transformed such that g(x) = f(–2x3). How does the graph of g(x) compare to the graph of f(x)?

A
g(x) is stretched horizontally and reflected over the y-axis.
B
g(x) is stretched horizontally and reflected over the x-axis.
C
g(x) is compressed horizontally and reflected over the y-axis.
D
g(x) is compressed horizontally and reflected over the x-axis.
3

The graph of the parent function f(x) = x3 is translated to form the graph of g(x) = (x − 4)3 − 7. The point (0, 0) on the graph of f(x) corresponds to which point on the graph of g(x)?

A
(4, −7)
B
(−4, −7)
C
(4, 7)
D
(−4, 7)
4

Graph the function y=x3+6x2+2x-11. Based on the graph, what is the largest possible x-value if y=0? Round your answer to the nearest hundredth, if necessary.

A
1.11
B
1.9
C
5.2
D
13.2
5

Which statements correctly describe the graph of the function f(x) = x3 – 2x2 – 19x + 20? Select three options.

Question illustration
A
As the x-values increase, the y-values always increase.
B
As x approaches negative infinity, y approaches negative infinity.
C
The domain of the function is all real numbers.
D
The range of the function is y 20.
Option D
E
The graph has a positive y-intercept.
6

The graph of f(x) = x3 – 6x2 + 9x is shown.

Question illustration
A
x = 3
B
x = –3, 0
C
x = 0, 3
D
x = –3, 0, 3
7

The graph of the parent function f(x) = x3 is translated to form the graph of g(x) = (x – 1)3 + 2. Which is the graph of g(x), the translated function?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
8

Which best describes the graph of the cubic function f(x) = x3 + x2 + x + 1?

A
As x increases, y increases along the entire graph.
B
As x increases, y increases, decreases, and then increases again.
C
As x increases, y decreases, increases, and then decreases again.
D
As x increases, y decreases along the entire graph.
9

Which is the graph of the function f(x) = x3 + x2 + 4?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
10

Which is the graph of the function f(x) = x3 + 6x2 + 11x + 6?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
11

The graph of f(x) = x3 – 3x2 + 4 is shown.

Question illustration
A
no real number solution
B
one real number solution
C
two real number solutions
D
three real number solutions
12

Which is the graph of the function f(x) = 2x3 – 7x2 + 2x + 3?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
13

The graph of the parent function f(x) = x3 is translated to form g(x) = (x – 7)3 + 9. The point (0, 0) on the graph of f(x) corresponds to which point on the graph of g(x)?

A
(7, 9)
B
(–7, 9)
C
(9, 7)
D
(9, –7)
14

Which is the graph of the function f(x) = 2x3 – 7x2 + 2x + 3?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
15

The graph of the parent function f(x) = x3 is transformed such that . Which statements about the graph of g(x) are accurate? Select three options.The graph does not pass through the origin.As x approaches negative infinity, the graph of g(x) approaches infinity.As x approaches infinity, the graph of g(x) approaches infinity.The domain of the function is all real numbers.The range of the function is all real numbers.

Question illustration
A
The graph does not pass through the origin.
B
As x approaches negative infinity, the graph of g(x) approaches infinity.
C
As x approaches infinity, the graph of g(x) approaches infinity.
D
The domain of the function is all real numbers.
E
The range of the function is all real numbers.
16

The graph of f(x) = x3 − 7x − 6 is shown.

Question illustration
A
x = −6
B
x = −2, −1
C
x = −2, −1, 3
D
x = −6, −2, −1, 3
17

Graph the function f(x) = x3 – 4x – 1. Which are approximate solutions for x when f(x) = 0? Select three options.–2.11–1.86–0.250.252.11

A
–2.11
B
–1.86
C
–0.25
D
0.25
E
2.11
18

The graph of the parent function f(x) = x3 is transformed such that . Which statements about the graph of g(x) are accurate? Select three options.

Question illustration
A
The graph does not pass through the origin.
B
As x approaches negative infinity, the graph of g(x) approaches infinity.
C
As x approaches infinity, the graph of g(x) approaches infinity.
D
The domain of the function is all real numbers.
E
The range of the function is all real numbers.
19

Graph the function y=x3+6x2+2x-11. Based on the graph, what is the largest possible x-value if y=0? Round your answer to the nearest hundredth, if necessary.

A
1.11
B
1.9
C
5.2
D
13.2
20

The graph of f(x) = x3 + x2 – 9x – 9 is shown.

Question illustration
A
x = –1, 3
B
x = –3, –1
C
x = –3, –1, 3
D
x = –9, –3, –1, 3

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