Question 8
For each real number $r$ let $T_{r}$ be the transformation of the plane that takes the point $(x, y)$ into the point $(2^{r} x, r 2^{r} x + 2^{r} y)$. Let $F$ be the family of all such transformations i.e. $F = \{ T_{r} : r \text{ a real number} \}$. Find all curves $y = f(x)$ whose graphs remain unchanged by every transformation in $F$.