College Algebra / Unit 5 Alg 290 worked example, 60 to 90 seconds
Graphing by Transformations
The idea
Graphing by transformations means reading a formula as edits to a parent function — horizontal moves from inside, vertical moves from outside — and applying stretches and reflections before shifts.
In practice
Graph g(x) = 2(x − 1)² + 3 from the parent f(x) = x². Inside first: (x − 1) slides the graph right 1. Outside next, in order: the 2 stretches outputs vertically, then the +3 lifts everything 3. Track one point through the pipeline: the parent's (1, 1) moves right to (2, 1), stretches to (2, 2), lifts to (2, 5) — and the check confirms it: g(2) = 2(1)² + 3 = 5. The vertex rides from (0, 0) to (1, 3), and g(1) = 3 agrees. One tracked point plus the vertex catches nearly every ordering mistake.
Where people slip
Stretch before shift on the outside; a lifted graph stretched afterward lifts twice.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
Builds on
- Nothing. This is a starting point.
Unlocks
- Nothing yet depends on this.
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