AnswersAlgebra IICubic and Cube Root Functions and Equations

Cubic and Cube Root Functions and Equations — Test Answers

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1
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Which is the function g of x for a restricted domain?

A
g of x is equal to cube root of x minus 4 ; x is greater than or equal to 0
B
g of x is equal to cube root of x minus 4 ; x is greater than or equal to negative 4
C
g of x is equal to cube root of x plus 4 ; x is greater than or equal to negative 4
D
g of x is equal to cube root of x plus 4 ; x is greater than or equal to 0
2
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Which equation represents h of x ?

A
h of x is equal to cube root of x plus 2
B
h of x is equal to cube root of x minus 2
C
h of x is equal to cube root of x plus 2
D
h of x is equal to cube root of x minus 2
3

What is the domain of the graphed function?

A
start set x such that x is a real number end set
B
start set y such that y is a real number end set
C
start set x such that 1 is less than x comma x is less than 5 end set
D
start set y such that 1 is less than y comma y is less than 5 end set
4

What is the solution to the equation square root of w squared plus 7 w minus 39 end root is equal to square root of 10 w plus 1 end root ?

A
w is equal to negative 5
B
w is equal to negative 8
C
w is equal to 8
D
w is equal to 5
6

Which is the graph of the function f of x is equal to x cubed plus x squared plus x plus 1 ?

A
Image with description On a coordinate plane, a curve increases through the point negative 1 comma negative 2, has a point of inflection at 0 comma negative 1, and increases through the point 1 comma 2.
B
Image with description On a coordinate plane, a curve increases through the point 0 comma negative 5, has a point of inflection at 1.5 comma 0.5, and increases through the point 2 comma 1.
C
Image with description On a coordinate plane, a curve increases through the point 1 comma negative 2, has a point of inflection at 1.5 comma negative 1.5, and increases through the point 2.5 comma 0.
D
Image with description On a coordinate plane, a curve increases through the point negative 2 comma negative 5, has a point of inflection at negative 0.5 comma 0.5, and increases through the point 2 comma 5.
7

What is the solution to the equation square root of 5 x minus 7 end root is equal to square root of 3 x plus 5 end root ?

A
x is equal to 6
B
x is equal to 12
C
x is equal to 1
D
x is equal to 24
8

What is the extraneous solution to the equation square root of 2 p plus 1 end root plus 2 square root of p is equal to 1 ?

A
p is equal to 4
B
p is equal to 0
C
p is equal to negative 2
D
p is equal to negative 4
9

The graph of the parent function f of x is equal to x cubed is translated to form the graph of g of x is equal to open paren x minus 1 close paren cubed plus 2 Which is the graph of g of x , the translated function?

A
Image with description On a coordinate plane, the graph of the parent cubic function is shifted 1 unit left and 2 units down.
B
Image with description On a coordinate plane, the graph of the parent cubic function is shifted 1 unit right and 2 units up.
C
Image with description On a coordinate plane, the graph of the parent cubic function is shifted 2 units right and 1 unit up.
D
Image with description On a coordinate plane, the graph of the parent cubic function is shifted 2 units left and 1 unit down.
10

Which of the following describes the solution to the equation square root of c squared plus 2 c minus 4 end root is equal to square root of 1 minus 2 c end root ?

A
negative 5 is an extraneous solution, and 1 is a true solution.
B
Both negative 5 and 1 are extraneous solutions.
C
Both negative 5 and 1 are true solutions.
D
negative 5 is a true solution, and 1 is an extraneous solution.
11

Which is the graph of the cube root function f of x is equal to cube root of x ?

A
Image with description On a coordinate plane, a cube root function goes through negative 4 comma negative 2, has an inflection point at 0 comma 0, and goes through 4 comma 2.
B
Image with description On a coordinate plane, a cube root function goes through negative 4 comma 2, has an inflection point at 0 comma 0, and goes through 4 comma negative 2.
C
Image with description On a coordinate plane, a cube root function goes through negative 8 comma 2, has an inflection point at 0 comma 0, and goes through 8 comma negative 2.
D
Image with description On a coordinate plane, a cube root function goes through negative 8 comma negative 2, has an inflection point at 0 comma 0, and goes thorugh 8 comma 2.
12

Which describes how to graph g of x is equal to cube root of x minus 5 plus 7 by transforming the parent function?

A
Translate the parent function 5 units down and 7 units to the right.
B
Translate the parent function 5 units to the right and 7 units up.
C
Translate the parent function 5 units to the left and 7 units up.
D
Translate the parent function 5 units up and 7 units to the right.
13

Which statement is true of the function f of x is equal to negative cube root of x ? Choose three correct answers.

A
The function has a domain of all real numbers.
B
The function has a range of start set y such that negative infinity is less than y comma y is less than infinity end set .
C
The function is always increasing.
D
The function passes through the point 3 comma negative 27 .
E
The function is a reflection of y is equal to cube root of x .
14

Which equation results from isolating a radical term and squaring both sides of the equation for the equation square root of x plus 6 end root plus square root of x is equal to 8 ?

A
x plus 6 is equal to 64 minus x
B
x plus 6 is equal to 64 plus x minus 16 square root of x
C
x plus 6 is equal to 64 plus x plus 16 square root of x
D
x plus 6 is equal to 64 plus x
15

The function f⁡(x)=root(3, x) is reflected over the horizontal axis and then translated 6 units down to create the function g⁡(x) Complete the steps to explain how to graph the function g⁡(x) Enter your answers in the boxes.

Answer:

-∛x-6

16

The graph of the parent function f of x is equal to x cubed is translated to form the graph of g of x is equal to x plus 3 cubed minus 4 The point 0 comma 0 on the graph of f of x corresponds to which point on the graph of g of x ?

A
negative 3 comma negative 4
B
negative 3 comma 4
C
3 comma negative 4
D
3 comma 4
17

How was the graph of f of x is equal to cube root of x shifted to form the translation?

A
2 units left
B
2 units right
C
2 units up
D
2 units down
18

Which equation represents f of x ?

A
f of x is equal to cube root of x plus 6 plus 1
B
f of x is equal to cube root of x plus 6 minus 1
C
f of x is equal to cube root of x minus 6 plus 1
D
f of x is equal to cube root of x minus 6 minus 1
19

Which statement is true?

A
The function is always decreasing.
B
The function is always increasing.
C
The function is only increasing when x is greater than or equal to 0 .
D
The function is only increasing when x is greater than or equal to negative 8 .
20

What is the range of the graphed function?

A
start set y such that y is a real number end set
B
start set y such that negative 2 is less than y comma y is less than 2 end set
C
start set x such that x is a real number end set
D
start set x such that negative 2 is less than x comma x is less than 2 end set
21

Based on the graph, how many distinct real number solutions does the equation x cubed plus 6 x squared plus 12 x plus 8 is equal to 0 have?

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

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