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.

The correct option is D.

Step-by-step explanation:

The cubic parent function is

The given function is

It i can be written as

               .... (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

               .... (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

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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step-by-step explanation: