B.5 Higher-Level FunctionsHL
HL-only extensions to the function toolkit: polynomial roots via the factor / remainder theorems and Vieta's formulas; rational functions including oblique asymptotes; even, odd, and self-inverse functions; solving inequalities g(x) ≥ f(x) and modulus equations |x − a|; sketching y = |f(x)|, y = f(|x|), and y = 1/f(x) from y = f(x).
Polynomial functions — factor, remainder, and rootsHLSign up
Factor and remainder theorems · Sums and products of roots — Vieta's formulas
Rational functions — graphs and asymptotesHLSign up
Rational functions (ax + b)/(cx² + dx + e) · Rational functions (ax² + bx + c)/(dx + e) — including oblique asymptotes
Symmetry and inverses — even, odd, self-inverseHLSign up
Even and odd functions · Inverse functions with domain restriction; self-inverse functions
Solving inequalities — g(x) ≥ f(x) and modulus equationsHLSign up
Solving g(x) ≥ f(x) graphically and analytically · Equations and inequalities involving |x − a|
Modulus and reciprocal of a functionHLSign up
Sketching y = |f(x)| and y = f(|x|) · Sketching y = 1/f(x) from y = f(x)