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Exponential & logarithmic graphs — the four shapes

A nine-scene guided mini-lesson: learn the 4 basic shapes, watch a curve flip in each axis, then sketch any y = lg(x − a) the exam way — asymptote, shape, draw, intercepts. Prev / Next drives the story (← → keys work too) — or press ▶ Play all.
1 · asymptote:  let 2 − x = 0  ⇒  x = 2 — inside the log = 0
2 · shape:  minus in front of x  ⇒  follows y = ln(−x) — any base
3 · draw:  that shape, hugging x = 2
4 · y-intercept:  sub x = 0:  y = ln 2 ≈ 0.693
   x-intercept:  sub y = 0:  ln(2 − x) = 0 ⇒ 2 − x = e0 = 1 ⇒ x = 1