Question

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.

Answer 1

its very hard to explain it with out a visual representation but if you put that in standard for to translate it into slope intercept form and put it on the grid the rest should be a piece of cake.

Answer 2

The correct option is D.

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.