Calculus doesn't ask you to learn a new kind of mathematics before it asks you to learn calculus — it asks you to get fast and confident with the algebra you already have, because you're about to use it constantly, under time pressure, while also thinking about something new. A limit problem that takes you thirty seconds to factor is a limit problem. The same problem, if the factoring takes you five minutes, quietly becomes an algebra problem wearing a calculus costume.
This chapter doesn't teach anything new. Every idea in it — functions, graphs, inverses, exponentials and logs, the unit circle, factoring, radicals, difference quotients — was already taught, carefully, in College Algebra, and every practice question here is pulled directly from that course rather than rewritten from scratch. Think of it as tuning an instrument you already know how to play, not learning a new one. The sections are short on purpose: enough to jog the memory and catch the rusty spots, not enough to feel like a whole course crammed into a week.
Two ideas get a little more attention than the rest, because the entire rest of this course leans on them constantly. Composing and decomposing functions — not just building f(g(x)) from f and g, but looking at a function and seeing the two (or three) simpler machines chained inside it — is the skill the chain rule needs, three chapters from now. And the difference quotient, \dfrac{f(x+h)-f(x)}{h}, isn't just another algebra exercise: it's the formula the very next chapter builds the entire idea of a limit out of.
By the end of this chapter, the toolkit is sharp, and the next chapter can spend its energy on what's new — not on relearning how to factor a trinomial in the middle of a limit problem.