AnswersAlgebra 2 with ProbabilitySquare Root and Cube Root Functions

Square Root and Cube Root Functions — Test Answers

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1
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What integer represents the horizontal translation of f of x to g of x ?

Answer:

-4

2
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Complete the last step by simplifying the expression. What is square root of 180 simplified?

A
30
B
6 times square root of 5
C
6
D
30 times square root of 5
3

What is the simplest form of square root of 1 comma 764 ?

A
2 squared times 3 squared times 7 squared
B
21
C
42
D
3 squared times 7 squared
4

What is the simplest form of square root of three comma zero two five ?

A
16
B
55
C
5 squared times 11 squared
D
5 squared plus 11 squared
5

What is the domain of the function?

A
all real numbers greater than but not equal to 0
B
all real numbers less than or equal to 0
C
all real numbers greater than or equal to 0
D
all real numbers
6

Complete the last step by simplifying the expression. What is square root of 3,150 end root simplified?

A
14
B
15 times square root of 14
C
14 times square root of 15
D
15
7

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

A
2 units down
B
2 units up
C
2 units right
D
2 units left
8

What is the domain of the function?

A
all real numbers less than 0
B
all real number less than or equal to 0
C
all real numbers greater than or equal to 0
D
all real numbers
9

What is the range of the function?

A
all real numbers greater than 0
B
all real number less than or equal to 0
C
all real numbers greater than or equal to 0
D
all real numbers
10

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 minus 1
D
f of x is equal to cube root of x minus 6 plus 1
11

If the range of f of x is equal to square root of m x and the range of g of x is equal to m square root of x are the same, which statement is true about the value of m ?

A
m can be any real number.
B
m can only equal 1 .
C
m can be any positive real number.
D
m can be any negative real number.
12

What is the simplified form of sqrt(10,000⁢x^64) ?

A
five-thousand x to the thirty-second power
B
one-hundred x to the eighth power
C
five-thousand x to the eighth power
D
one-hundred x to the thirty-second power
13

What is the simplified form of square root of four hundred x to the hundredth power end root ?

A
two hundred x to the fiftieth power
B
twenty x to the fiftieth power
C
two hundred x to the tenth power
D
twenty x to the tenth power
15

Which is the graph of g of x is equal to square root of x minus 16 end root ?

A
Image with description A coordinate plane with x-axis labeled from 4 to 44 in increments of 4 and y-axis labeled from 1 to 10 in increments of 1. A smooth curve originates from 16 comma 0, moves right and passes through the points 20 comma 2 and terminates at the point 40 comma 5.
B
Image with description A coordinate plane displays the x-axis labeled from 4 to 44 in increments of 4 and the y-axis labeled from 1 to 10 in increments of 1. An increasing curve begins at approximately 0 comma 4, rises steeply at first, then gradually levels off, passing near 4 comma 6, 12 comma 7.5, 24 comma 9, and ending at approximately 36 comma 10.
C
Image with description A coordinate plane with x-axis labeled from 4 to 44 in increments of 4 and y-axis labeled from 1 to 10 in increments of 1. A smooth curve originates from 4 comma 0, moves right and passes through the point 20 comma 4 and terminates at the point 40 comma 6.
D
Image with description A coordinate plane displays the x-axis labeled from 4 to 44 in increments of 4 and the y-axis labeled from 1 to 10 in increments of 1. An increasing curve begins at approximately 4 comma 4, rises steeply at first, then gradually levels off, passing near 8 comma 6, 16 comma 7.5, 28 comma 9, and ending at approximately 40 comma 10.
16

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 to the right and 7 units up.
B
Translate the parent function 5 units to the left and 7 units up.
C
Translate the parent function 5 units down and 7 units to the right.
D
Translate the parent function 5 units up and 7 units to the right.
17

Which of the following describes the graph of y is equal to cube root of 8 x minus 64 minus 5 compared to the parent cube root function?

A
stretched by a factor of 8 and translated 8 units right and 5 units down
B
stretched by a factor of 2 and translated 64 units right and 5 units down
C
stretched by a factor of 8 and translated 64 units right and 5 units down
D
stretched by a factor of 2 and translated 8 units right and 5 units down
18

What is the range of the function f of x is equal to square root of x plus 3 minus 7 ?

A
f of x is greater than or equal to 7
B
f of x is greater than or equal to negative 7
C
f of x is greater than or equal to negative 3
D
f of x is greater than or equal to 3
20

Which graph represents y is equal to cube root of x ?

A
Image with description On a coordinate plane, the x and y axes ranging from negative 9 to 9 in increments of 1, with major tick marks at even integers. A parabolic curve, opening upwards, has its vertex at the origin (0 comma 0). The curve passes through points such as (1 comma 1), (negative 1 comma 1), (2 comma 4), and (negative 2 comma 4).
B
Image with description On a coordinate plane, the x and y axes ranging from negative 9 to 9 in increments of 1, with major tick marks at even integers. A curve starts at the origin (0 comma 0). The curve extends upwards and to the right, passing through points (1 comma 1), (4 comma 2) and (8 comma 3) in first quadrant.
C
Image with description On a coordinate plane, the x and y axes ranging from negative 9 to 9 in increments of 1, with major tick marks at even integers. A curve passes through the origin (0 comma 0). The curve increases from the bottom left to the top right, passing through points such as (negative 2 comma negative 8), (negative 1 comma negative 1), (1 comma 1), and (2 comma 8).
D
Image with description On a coordinate plane x and y axes range from negative 9 to 9 in increments of 1. A graph of cubic function passes through points (negative 8 comma negative 2), (0 comma 0), and (8 comma 2). The curve has a point of inflection at the origin.
21

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 range of start set y such that negative infinity is less than y comma y is less than infinity end set .
B
The function is always increasing.
C
The function passes through the point 3 comma negative 27 .
D
The function is a reflection of y is equal to cube root of x .
E
The function has a domain of all real numbers.
22

Which of the following is the graph of y is equal to square root of negative x minus 3 end root ?

A
Image with description On a coordinate plane x and y axes range from negative 9 to 9 in increments of 1. The curve opens down and to the left in quadrant 2. The origin of the curve is (negative 3 comma 0) and passes through (negative 7 comma 2).
B
Image with description On a coordinate plane, the x and y axes range from negative 9 to 9 with increments of 1. The curve opens up and to the right in quadrants III and IV. The origin of the curve is negative 3 comma 0. The curve passes through the point 0 comma 1 point 6 and 6 comma negative 3, and end at 9 comma negative 3 point 5. The arrow is present on both end of the curve.
C
Image with description On a coordinate plane x and y axes range from negative 9 to 9 in increments of 1. The curve originates from (3 comma 0) and passes through points (negative 1 comma 2) and (negative 6 comma 3) in the 2nd quadrant.
D
Image with description On a coordinate plane x and y axes range from negative 9 to 9 in increments of 1. The curve originates from (3 comma 0) and decreases into the fourth quadrant. It passes through points (4 comma negative 1) and (7 comma negative 2).

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