functional equations - What are all the functions that satisfy $f(x)/f(y) = f(kx)/f(ky)$?

Find all continuous functions defined over real numbers that satisfy

$\frac{f(x)}{f(y)} = \frac{f(kx)}{f(ky)}$,

for any $x$ and $y$. It is possible to show that the above condition holds for $f(x) = ax^b$ since

$\frac{ax^b}{ay^b} = \frac{ak^bx^b}{ak^by^b}$.

Do functions that satisfy this property have a specific name?