The graph of the function f(x) = x2 is shown. compared to this, how would the graph of a function g appear, if g(x) = f(2x)?

The graph would be shrunk by a factor of 4.

Replacing x with 2x, we would have f(2x) = 4x².  The value of a, 4, tells us it will be either a stretch or a shrink; if a>1, it is a shrink; if a<1, it is a stretch.