Graphing Radical Functions Answers

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1
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Which of the following describes the graph of the transformed function compared with the parent function? Select all that apply.

A
reflected over the x-axis
B
translated 2 units left
C
translated 2 units right
D
compressed by a factor of 0.4
E
stretched by a factor of 0.4
F
translated 2 units up
G
translated 2 units down
2
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The domain of is all real numbers.x >= -5.x >= -1.x >= 1.✔ x >= 5.

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A
all real numbers.
B
x >= -5.
C
x >= -1.
D
x >= 1.
E
✔ x >= 5.
3

The range of is all real numbers.y >= -5.✔ y >= -1.y >= 1.y >= 5.

Question illustration
A
all real numbers.
B
y >= -5.
C
✔ y >= -1.
D
y >= 1.
E
y >= 5.
4

Which is the graph of

Question illustration
A
graph A
B
graph B
C
graph C
D
graph D
6

The graph is not reflected.✔ reflected over the x-axis.reflected over the y-axis.

A
not reflected.
B
✔ reflected over the x-axis.
C
reflected over the y-axis.
7

The graph has a vertical stretch by a factor of 1/3.compression by a factor of 1/3.✔ stretch by a factor of 3.compression by a factor of 3.

A
stretch by a factor of 1/3.
B
compression by a factor of 1/3.
C
✔ stretch by a factor of 3.
D
compression by a factor of 3.
14

Explain how to rewrite the function shown in order to determine the transformation of the parent function. Then, describe the transformation of the graph compared to the parent function.

Question illustration
Answer:

Factor −8 from the radicand to rewrite the function as y = −2∛(x + 1/2). This reflects the parent graph over the x-axis, stretches it vertically by a factor of 2, and shifts it 1/2 unit to the left.

15

Reread your description. Did it include the following?

A
Rewrite the equation by factoring –8 from the radicand and taking the cube root to get –2 in front of the radical symbol.
B
The graph is reflected over the x-axis.
C
The graph is also reflected over the y-axis.
D
The graph is vertically stretched by a factor of 2.
E
The graph is translated ½ unit to the left.

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