Apply $D(x,y)=(cx,cy)$ to the graph of $y=x^2$ and find the equation of the transformed graph. Hint: Let $u=cx$ and write $v=cx^2$ in terms of $u$. 



What I think the answer is: 

$y=x^2$ is the same as $(x, x^2)$ therefore, applying $D$ to the equation gives us $(cx, (cx)x=cx^2)$, that is, $y=cx^2$.
According to the given hint, $x = \dfrac {u}{c}$.

Expressing v in terms of u, we should have $v = cx^2 = c (\dfrac {u}{c})^2 = \dfrac {u^2}{c}$. Then, $y = \dfrac {x^2}{c}$.
According to the given hint, $x = \dfrac {u}{c}$.

Expressing v in terms of u, we should have $v = cx^2 = c (\dfrac {u}{c})^2 = \dfrac {u^2}{c}$. Then, $y = \dfrac {x^2}{c}$.