AnswersAlgebraic ReasoningThe Cube Root Function

The Cube Root Function — Quiz Answers

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Which statements describe the graph of y is equal to cube root of x minus 1 plus 2 ? Choose three correct answers.

A
The graph has a range of y is greater than or equal to 1 .
B
As x is increasing, y is decreasing.
C
The graph has a domain of all real numbers.
D
The graph has a y -intercept at 0 comma 1 .
E
The graph has an x -intercept at negative 7 comma 0 .
2
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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 8 comma negative 2, has an inflection point at 0 comma 0, and goes thorugh 8 comma 2.
B
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.
C
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.
D
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.
3

What is the domain of f of x is equal to cube root of x ?

A
whole numbers
B
positive numbers and zero
C
all integers
D
all real numbers
4

The graph of y is equal to cube root of x is reflected over the y -axis and then translated down 2 units to form f of x Which is the graph of f of x ?

A
Image with description On a coordinate plane, the x-axis ranges from negative 10 to 10 in increments of 2, and the y-axis ranges from negative 5 to 5 in increments of 1. A curve goes through the point negative 3 comma negative 1, the point negative 2 comma 0, and the point negative 1 comma 1.
B
Image with description On a coordinate plane, the x-axis ranges from negative 10 to 10 in increments of 2, and the y-axis ranges from negative 5 to 5 in increments of 1. A curve goes through the point negative 1 comma negative 1, the point 0 comma negative 2, and the point 1 comma negative 3.
C
Image with description On a coordinate plane, the x-axis ranges from negative 10 to 10 in increments of 2, and the y-axis ranges from negative 5 to 5 in increments of 1. A curve goes through the point 1 comma 1, the point 2 comma 0, and the point 3 comma negative 1.
D
Image with description On a coordinate plane, the x-axis ranges from negative 10 to 10 in increments of 2, and the y-axis ranges from negative 5 to 5 in increments of 1. A curve goes through the point negative 1 comma 1, the point 0 comma 2, and the point 1 comma 3.
5

Which cube root function is always decreasing as x increases?

A
f of x is equal to negative cube root of x plus 5
B
f of x is equal to cube root of x minus 8
C
f of x is equal to cube root of x minus 5
D
f of x is equal to cube root of negative open paren 5 minus x close paren
6

Which is the graph of y is equal to cube root of x plus 1 minus 2 ?

A
Image with description On a coordinate plane, a cube root function goes through negative 6 comma 2, has an inflection point at 2 comma 0, and goes through 10 comma negative 2.
B
Image with description On a coordinate plane, a cube root function goes through negative 8 comma 0, has an inflection point at 0 comma 2, and goes through 8 comma 4.
C
Image with description On a coordinate plane, a cube root function goes through negative 10 comma negative 2, has an inflection point at negative 2 comma 0, and goes through 6 comma 2.
D
Image with description On a coordinate plane, a cube root function goes through negative 8 comma 0, has an inflection point at 0 comma negative 2, and goes through 8 comma negative 4
7

The function s times cap v is equal to cube root of cap v describes the side length, in units, of a cube with a volume of cap 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?

A
s is greater than or equal to 4
B
s is greater than or equal to 8
C
s is greater than or equal to 16
D
s is greater than 0
8

The function f of x is equal to cube root of x is reflected over the x -axis to create the graph of g of x is equal to negative cube root of x Which is the graph of g of x ?

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

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