IB Maths: Functions Revision

Functions is a core part of IB Maths. Revise the key concepts and common mistakes below, then lock them in with the free games.

Key concepts

Standard formy = ax^2 + bx + c, with a ≠ 0.

Vertex formy = a(x - h)^2 + k with vertex (h, k).

DiscriminantΔ = b^2 - 4ac determines root nature.

Quadratic formulax = (-b ± √(b^2 - 4ac)) / (2a).

Axis of symmetryVertical line x = -b/(2a) through vertex.

Completing squareRewrite ax^2 + bx + c into vertex form.

Exponential functionf(x) = e^x grows continuously with base e.

Natural logln(x) = log_e(x), inverse of e^x.

Modulus|x| = x if x ≥ 0, else -x; always non-negative.

Vertical translationf(x) + k shifts graph up by k units.

Horizontal stretchf(x/a) stretches horizontally by factor a.

Reflection-f(x) flips across x-axis; f(-x) across y-axis.

DomainSet of all valid input x-values of a function.

RangeSet of all possible output y-values of a function.

Learn Functions step by step

Free interactive mini-lessons: short screens, worked examples and quick checks. Pick your exam board to open its course map, then tap L on this topic:

IB Mathematics: Analysis & Approaches · HL IB Mathematics: Analysis & Approaches · SL IB Mathematics: Applications & Interpretation · HL IB Mathematics: Applications & Interpretation · SL

Practise Functions — free games

Test yourself with these quick revision games for this topic:

▶ Two Truths, One Lie ▶ Reveal Race ▶ Connections Grid ▶ Falling Words ▶ Word Web

See all 22 games in the Revision Arcade →

More IB Maths topics

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