AnswersAISD Algebraic Reasoning A Credit Recovery 2026-2027Modeling Functions Using Finite Differences

The Cubing Function Answers

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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
2
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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
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)?

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.
4

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
5

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
6

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

Question illustration
A
g(x) = (x + 4)3 + 6
B
g(x) = (x – 4)3 + 6
C
g(x) = (x + 6)3 – 4
D
g(x) = (x – 6)3 – 4
7

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
8

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.
9

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)
10

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.

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