NapkinCalc

Precalculus A — Functions & Transformations

Transformations

continues from lesson 2 — values defined earlier in the course stay live here

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)
  • a·f(x) stretches it taller

The plot is f shifted right 2 and up 5 — edit the numbers and watch it move.

f(x - 2) + 5
10203040-202468

f(x − 2) + 5 — the same parabola, relocated

Real-world hook: transformations re-zero and re-scale real models — shifting a temperature curve to a new start time, converting °C↔°F (a stretch plus a shift), or moving a sound wave by a phase delay.