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