Mathematics: A.) reflect the parent function over the y-axis, and translate it 3 units to the right. b.) reflect the parent function over the y-axis, and translate it 3 units to the left. c.) reflect the parent function over the x-axis, and translate it 8 units to the right. d.) reflect the parent function over the x-axis, and translate it 8 units to the left.

I think the answer is D but I m not 100 percent sure. I hope this helpsStep-by-step explanation:I think I took this test before...

A.) reflect the parent function over the y-axis, and

ptrlvn01

05.01.2022

The correct option is D.

Step-by-step explanation:

The cubic parent function is

$f(x)=\sqrt[3]{x}$

The given function is

$h(x)=-\sqrt[3]{x+8}$

It i can be written as

h(x)=-f(x+8) .... (1)

The function h(x) is negative of function f(x+8), therefore the graph of parent function reflected over the x-axis.

The translation is defined as

h(x)=f(x+a)+b .... (2)

Where, a is horizontal shift and b is vertical shift.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

From (1) and (2) we get

a=8,b=0

Since a=8>0, therefore the graph shifts 8 units left.

The graph of parent function reflected over the x-axis, and translate it 8 units to the left.

Therefore the correct option is D.

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