Question

Consider the functions f(x)=4x^3 and g(x)=9x^3. Find a size change that maps f(x) onto g(x). Can someone help me with this?

Answer 1

Hints:
vertical scaling
\(g(x)=af(x)\) where a is a vertical scaling factor

horizontal scaling:
f(x)=\(4x^3=2^2x^3=(2^{2/3}x)^3\)
similarly
g(x)=\(9x^3=3^2x^3=(3^{2/3}x)^3\)
and
g(x)=f(bx) where b is a horizontal scale factor to be found.