Find and Draw $\ S=f^{-1}([0,+\infty))$ where $\ f(x,y)=y(x-y)\ $ 
Let $\ f:\mathbb{R^2}\rightarrow\mathbb{R}\ $ be given by $\ f(x,y)=y(x-y)\ $. Find and draw the pre-imiage $\ S=f^{-1}([0,+\infty))$.

I always try to include a response in my questions, but I am unsure how to attempt this question. I don't quite understand how to start this question. Is there some intuition/method that I can use?

You want all points $(x,y)$ satisfying $y(x-y)\geq 0$. There are two cases to analyse:
1) $y\geq 0$ and $x-y\geq 0$ : These inequalities describe the region bellow the graphic of $y=x$ such that $y\geq 0$.
 2) $y\leq 0$ and $x-y\leq 0$ : These inequalities describe the region above the graphic of $y=x$ such that $y\leq 0$.
So the region described is the one between the lines $y=x$ and $y=0$.
