Having visuals for the examples helped a lot. Continuing this throughout the class would be greatly appreciated.

Yep, there will be plenty of visuals as we continue... this is computer graphics, after all! :-)

I can't say I'm a big fan of the f(x) notation for functions. I think it's probably more consistent to just call them by their single letter names, i.e "f" or "g". Writing them this way makes it easier to treat them as just regular mathematical objects without introducing spurious (x)s everywhere that can be a bit confusing. It can get especially confusing when you have, say, x+y as inputs to a function that's being notated as f(x), and then one needs to mentally rename the parameter of f before doing the substitution... almost got me a few times on the homework.

@grantwu Yep, and that's a particularly relevant perspective when thinking of functions as elements of a vector space (who cares about the arguments?). It's always a trade-off between being explicit-but-verbose and implicit-but-concise.