Apply $D(x,y)=(cx,cy)$ to the graph of $y=x^2$ and find the equation of the transformed graph.

Question

Hint: Let $u=cx$ and write $v=cx^2$ in terms of $u$.

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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, $y=cx^2$.

Answer 1

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, $y = \dfrac {x^2}{c}$.