Suppose f(x)= x^2 and g(x)=(1/3x)^2 which statement best compares the graph of g(x) with the graph of f(x) a) the graph of g(x) is horizontally compressed by a factor of 3 b) the graph of g(x) is horizontally stretched by a factor of 3 c) the graph of g(x) is shifted 3 units to the right d)the graph of g(x) is vertically compressed by a factor of 3

The rules for linear transformations are that
  g(x) = a·f(b·(x-c)) +d
stretches the graph vertically by a factor of "a" (before the shift)
compresses the graph horizontally by a factor of "b" (before the shift)
shifts it to the right by amount "c"
shifts it up by amount "d".

Your equation has b=1/3, so the graph is compressed by a factor of 1/3, which is equivalent to a stretch by a factor of 3.

The appropriate choice of description is ...
  b) the graph of g(x) is horizontally stretched by a factor of 3