AnswersRecovery Content Sec Math 3 - Quarter 4 - 202627Domain and Range

The Cubing Function Answers

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1
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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
2
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The graph of f(x) = x3 – 6x2 + 9x is shown.

Question illustration
x
x = 3
x
x = –3, 0
x
x = 0, 3
x
x = –3, 0, 3
3

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)?

g
g(x) is stretched horizontally and reflected over the y-axis.
g
g(x) is stretched horizontally and reflected over the x-axis.
g
g(x) is compressed horizontally and reflected over the y-axis.
g
g(x) is compressed horizontally and reflected over the x-axis.
4

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)?

(
(7, 9)
(
(–7, 9)
(
(9, 7)
(
(9, –7)
5

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)?

(
(4, −7)
(
(−4, −7)
(
(4, 7)
(
(−4, 7)
6

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.

1
1.11
1
1.9
5
5.2
1
13.2
7

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
8

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

Question illustration
x
x = −6
x
x = −2, −1
x
x = −2, −1, 3
x
x = −6, −2, −1, 3
9

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.
10

The parent function f(x) = x3 and a translation, g(x), are shown on the graph.

Question illustration
g
g(x) = (x + 4)3 + 6
g
g(x) = (x – 4)3 + 6
g
g(x) = (x + 6)3 – 4
g
g(x) = (x – 6)3 – 4
11

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.
12

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

A
–2.11
B
–1.86
C
–0.25
D
0.25
E
2.11
13

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
14

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?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D

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