Question

PLEASE HELP !! suppose that F(x)=x^2 and G(x)=3x^2+8.which statement best compares the graph of G(x) with the graph of F(x)

Answer 1

That '3' will stretch the graph vertically, and that +8 will shift the whole graph upward by 8 units. Why not try graphing these 2 functions?

Answer 2

The correct option is A.

Explanation:

The functions are

`F(x)=x^2` ... (1)

`G(x)=3x^2+8` .... (2)

The vertical stretch and compression is defined by

`G(x)=kF(x)`

If |k|>1, then function F(x) stretched vertically and if |k|<1, then function F(x) compressed vertically.

On comparing (1) and (2), we get k=3>1. It means graph of F(x) stretched vertically.

The shifting of function is defined as

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

If b>0, then function F(x) shifts b units upward and if b<0, then function f(x) shifts b units downward.

On comparing (1) and (2), we get b=8>0. It means graph of F(x) shifts 8 units up.

The graph of G(x) is the graph of F(x) stretched vertically and shifted 8 units up.

Therefore option A is correct.