Answer:
The correct option is A.
Step-by-step explanation:
The functions are
[tex]F(x)=x^2[/tex] ... (1)
[tex]G(x)=3x^2+8[/tex] .... (2)
The vertical stretch and compression is defined by
[tex]G(x)=kF(x)[/tex]
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
[tex]G(x)=F(x)+b[/tex]
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.
