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

The Cube Root Function Answers

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1
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What is the domain of f(x) = ?

Question illustration
A
all real numbers
B
positive numbers and zero
C
all integers
D
whole numbers
2
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The graph of g(x) is a reflection and translation of .

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A
g (x) = RootIndex 3 StartRoot x + 1 EndRoot
Option A
B
g (x) = RootIndex 3 StartRoot x minus 1 EndRoot
Option B
C
g (x) = Negative RootIndex 3 StartRoot x + 1 EndRoot
Option C
D
g (x) = Negative RootIndex 3 StartRoot x minus 1 EndRoot
Option D
3

Which cube root function is always decreasing as x increases?

A
f(x) =
Option A
B
f(x) =
Option B
C
f(x) =
Option C
D
f(x) =
Option D
4

The function s(V) = describes the side length, in units, of a cube with a volume of V cubic units. Jason wants to build a cube with a minimum of 64 cubic centimeters.What is a reasonable range for s, the side length, in centimeters, of Jason’s cube?

Question illustration
A
s > 0
B
s 4
Option B
C
s 8
Option C
D
s 16
Option D
5

The graph of g(x) is a translation of y = .

Question illustration
A
g(x) =
Option A
B
g(x) =
Option B
C
g(x) =
Option C
D
g(x) =
Option D
6

The graph shows the function f(x).

Question illustration
A
f(x) =
Option A
B
f(x) =
Option B
C
f(x) =
Option C
D
f(x) =
Option D
7

The function f(x) = is reflected over the x-axis to create the graph of g(x) = .Which is the graph of g(x)?

Question illustration
A
On a coordinate plane, a cube root function goes through (negative 2, negative 8), has an inflection point at (0, 0), and goes through (2, 8).
Option A
B
On a coordinate plane, a cube root function goes through (negative 2, 8), has an inflection point at (0, 0), and goes through (2, negative 8).
Option B
C
On a coordinate plane, a cube root function goes through (negative 8, 2), has an inflection point at (0, 0), and goes through (8, negative 2).
Option C
D
On a coordinate plane, a cube root function goes through (negative 8, negative 2), has an inflection point at (0, 0), and goes thorugh (8, 2).
Option D
8

On the coordinate grid, the graph of is shown. It is a translation of .

Question illustration
A
{x | 1 < x < 5}
B
{y | 1 < y < 5}
C
{x | x is a real number}
D
{y | y is a real number}
9

Which is the graph of the cube root function f(x) = ?

Question illustration
A
On a coordinate plane, a cube root function goes through (negative 8, 2), has an inflection point at (0, 0), and goes through (8, negative 2).
Option A
B
On a coordinate plane, a cube root function goes through (negative 8, negative 2), has an inflection point at (0, 0), and goes thorugh (8, 2).
Option B
C
On a coordinate plane, a cube root function goes through (negative 4, negative 2), has an inflection point at (0, 0), and goes thorugh (4, 2).
Option C
D
On a coordinate plane, a cube root function goes through (negative 4, 2), has an inflection point at (0, 0), and goes through (4, negative 2).
Option D
10

The graph of y = is reflected over the y-axis and then translated down 2 units to form f(x). Which is the graph of f(x)?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
11

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)
12

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
13

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.
14

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
15

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
16

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.
17

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
18

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)
19

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
20

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

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