Syllabus Map

AA HL Functions Syllabus Points

The official IB syllabus content covering AHL points 2.12 through 2.15:

  1. 2.12Polynomial functions, rational functions of form $f(x) = \frac{ax^2+bx+c}{dx+e}$, polynomial division, oblique (slant) asymptotes; graphs of $y = |f(x)|$ and $y = f(|x|)$
  2. 2.13Composite transformations; transformations yielding $y = \frac{1}{f(x)}$ and $y = [f(x)]^2$; odd and even functions symmetry
  3. 2.14Solving inequalities graphically and analytically: polynomial, rational, and modulus inequalities ($|f(x)| \le g(x)$)
  4. 2.15Composite functions and inverse functions with restricted domains

Study by topic

AHL Topic 2 Interactive Study Guides

Every guide features our standard 4-tab interface: Study Notes, Practice Exercises (10 tiered problems with collapsible solutions), Formula Sheet, and Mini Test (MCQs & exam FRQs).

2.12, 2.14 Modulus Functions & Inequalities Graphing $y = |f(x)|$ and $y = f(|x|)$, vertex points, piecewise definitions, and solving modulus equations and inequalities analytically and graphically. Open Interactive Guide 2.12 Rational Functions & Oblique Asymptotes Polynomial long division for rational curves where degree of numerator exceeds denominator by 1, finding oblique linear asymptotes $y = mx+c$, and asymptotic behavior. Open Interactive Guide 2.13 Composite Transformations & Reciprocal Graphs Sketching $y = \frac{1}{f(x)}$ and $y = [f(x)]^2$ from given graphs of $f(x)$, invariant points, asymptotic inversions, and odd vs even function algebraic testing. Open Interactive Guide

Prerequisite Knowledge

Core SL Foundation Prerequisites

Review the 7 standard level Topic 2 guides:

2.1 Straight Lines & Notation 2.2–2.4 Graphs & Key Features 2.5 Composite & Inverse 2.6–2.7 Quadratics & Discriminant 2.8 Rational Functions SL 2.11 Transformations SL