Question

The graph of F(x), shown below, has the same shape as the graph of G(x)=x^4 but it is shifted 4 units to the left. What is the equation?

Answer 1

G(x) = (x+4)^4 is the answer. It's D. last choice

G(x) = (x+4)^4 shifted F(x) = x^4 4 units to the left

Answer 2

The correct option is D.

Explanation:

The given function is

`G(x)=(x)^4`

It is given that the shape of F(x) and G(x) are same.

The transformation is defined as

`F(x)=G(x+a)+b`

`F(x)=(x+a)^4+b` ....(1)

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.

It is given that G(x) shifted four units left. It means a=4 and b=0.

Substitute a=4 and b=0 in equation (1).

`F(x)=(x+4)^4+0`

`F(x)=(x+4)^4`

The required function is
`F(x)=(x+4)^4`.

Therefore the correct option is D.