To answer this question we need to remember that if we multiply a function f(x) by a constant a>0 then we have a vertical strecth or compression of function f(x). We have the two following cases:
• If a>1 then the graph will be stretched.
,
• If a<1 then the graph will be compressed.
Now, in this case we know that the function f(x) is x^2 and we notice that the function g(x) is a vertical compression of function f(x).
Since f(2)=4 and we know that g(x)=2, then we conclude that the factor have to be 1/2; therefore:
[tex]g(x)=\frac{1}{2}x^2[/tex]
and the answer is D.
