Question

Suppose that F(x) = x^3 and G(x) = (4x)^3 − 5. Which statement best compares the graphs of F(x) and G(x)?

A.The graph of G(x) is the graph of F(x) stretched vertically and shifted 5 units down.
B.The graph of G(x) is the graph of F(x) stretched horizontally and shifted 5 units down.
C.The graph of G(x) is the graph of F(x) compressed vertically and shifted 5 units down.
D.The graph of G(x) is the graph of F(x) compressed horizontally and shifted 5 units down.

Answer 1

we have that
F(x) = x^3  and G(x) = (4x)^3 − 5
so
G(x) = F(4x) -5

the visual effect is
1) shrink horizontally by 1/4
2) shift down by 5

therefore 
the answer is the option
D.The graph of G(x) is the graph of F(x) compressed horizontally and shifted 5 units down.