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I was asked to
Draw the level sets of $$f(x,y,z) = 9x^2-4y^2-36z$$
I under how to draw them with just two variables, but does anyone have any resources that could help me visualize drawing these sets in 3D? I'm having trouble understanding what the answer would look like
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$\begingroup$Your idea is close, though, I presume you mean $z=\ldots$, rather than $x=\ldots$.
Note that a level set of your function has the form $f(x,y,z)=k$ for some real number $k$. For this particular function, that is $$9x^2-4y^2-36z = k$$ or $$z = \frac{9x^2-4y^2}{36}-\frac{k}{36}.$$ Presumably, you know that each of these is a hyperbolic paraboloid; the parameter $k$ simply shifts the paraboloid up or down. Here are a few of them sketched together:
