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Notation / compose
Function: Higher: f(x) is output; domain inputs, range outputs
Order: Higher: fg(x)=f(g(x)); nearest x first; fg need not equal gf
Inverse
Reverse: Higher: Solve y=f(x) for x; swap letters; not reciprocal
Restriction: Higher: One-to-one domain needed; x² with x ≥ 0 reverses to √x
Translations
Vertical / horizontal: Higher: f(x)+a moves up; f(x−a) moves right
Example: Higher: (x−2)²+3: right 2, up 3; minimum (2,3)
Reflection / check
Axes: Higher: −f(x): x-axis; f(−x): y-axis
Track: Higher: Move points AND asymptotes; verify domain and intercepts
