Precalculus A — Functions & Transformations
Part 1 of 2. Function notation, composition, graph transformations (shifts & stretches), and inverse functions.
Calculus studies how functions change — so first, get truly fluent in functions. A function is a machine: feed it one number, it returns exactly one number. This is part 1 of 2, and you can build and run real machines live.
- 01 Function notation ELI5: f(x) = x² − 3x names a machine; f(4) runs it (plug 4 in everywhere x appears). Once defined, every cell below can call it — no retyping the formula.
- 02 Composition — machines feeding machines ELI5: f(g(x)) wires g's output straight into f's input — two machines on an assembly line. Order matters: f(g(x)) is usually not the same as g(f(x)),…
- 03 Transformations ELI5: every graph move is just arithmetic on the formula: f(x) + k slides up by k f(x − h) slides right by h (yes, minus shifts right — it fools everyone once)…
- 04 Inverse functions ELI5: an inverse undoes the original — if f turns 5 into 16, then f⁻¹ turns 16 back into 5. Only one-to-one machines have inverses (each output from exactly…
next course: Precalculus B — Polynomials & Rational Functions →