“Inside moves it sideways backwards, outside moves it up” is the kind of rule students half-remember at the worst moment. On Desmos you don't recall the rule — you watch it happen.
The move: Type the new function, watch it move.
Why it works: f(x − h) + k literally redraws the graph shifted — the calculator shows the motion, so vertex questions about transformed functions become tap-and-read.
The pattern
- Define the parent f(x)
- Type the transformed / composed version
- Tap the point it asks for
Worked example: If f(x) = x², the graph of g(x) = f(x − 3) + 2 has its vertex at which point?
- Define the parent function.
f(x)=x^2 - Graph the transformed version right on top.
y=f(x-3)+2 - The parabola slid RIGHT 3 and UP 2. Tap the new vertex: (3, 2). The “minus means right” confusion dies here.
Worked example 2: If f(x) = 2x + 1 and g(x) = x², what is f(g(3))?
- Define both functions.
f(x)=2x+1,g(x)=x^2 - Type exactly what they ask: f(g(3)). Desmos prints 19.
f(g(3)) - (The trap answer 49 is g(f(3)) — order matters, and typing it literally protects you.)
g(f(3))
Remember it on test day
Type it, watch it move. That's the whole cue — say it when you see this question type and the steps follow.
When this isn't the move
Describing a transformation in words (multiple-choice about direction) still benefits from knowing the rule — use the graph to verify, not to guess.
Drill it until it's reflex
This move is one of Desvantage's 18 training modules: a plain-English lesson, a type-it-yourself walkthrough inside a live Desmos calculator, and a 100-question drill bank that deals ten fresh questions per round. The first two modules — plus the 12-question diagnostic — are free.