ANSWER
[tex]g(x) = 9 {x}^{2} [/tex]
EXPLANATION
The given function is:
[tex]f(x) = {x}^{2} [/tex]
The function g(x) is a vertical compression of f(x).
This implies that:
[tex]g(x)=a\bullet f(x)[/tex]
[tex]g(x)=a\bullet {x}^{2} [/tex]
The function g(x) goes through (1,9).
[tex]g(1)=9[/tex]
[tex]a\bullet {(1)}^{2} = 9[/tex]
[tex]a = 9[/tex]
Hence the function is:
[tex]g(x) = 9 {x}^{2} [/tex]
This can be rewritten as:
[tex]g(x) = {(3x)}^{2} [/tex]
The correct choice is A.
