Question

F(x)=x^2. What is g(x)?A. g(x)= 1/4x^2B. g(x)= (1/2x)^2C. g(x)= 2x^2D. g(x)= 1/2x^2

Answer 1

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:

`g(x)=(1)/(2)x^2`

and the answer is D.