IB Maths: Transformations of Graphs — Your Questions Answered

Graph transformations describe how the graph of $y=f(x)$ changes under a translation, stretch, or reflection — giving you $y=f(x)+a$, $y=f(x-a)$, $y=af(x)$, $y=f(ax)$, and $y=-f(x)$ or $y=f(-x)$. You're expected to sketch the new graph, state new coordinates, and find the transformed equation.

$f(x)+a$ shifts the whole graph vertically by $a$ units (up if $a>0$) — every $y$-value changes. $f(x+a)$ shifts it horizontally, but counter-intuitively left by $a$ if $a>0$. Mixing these two up is the single most common transformation error I see in mock papers.

Trig transformations use the same rules as any function, but examiners like to test them via $y=a\sin (b(x-c))+d$: $a$ changes amplitude, $b$ changes the period (period $=360°/b$ or $2\pi /b$), $c$ shifts the graph horizontally, and $d$ shifts it vertically, resetting the equilibrium line.

Transformations turn up in both Paper 1 and Paper 2, usually asking you to sketch an image graph, state new coordinates or asymptotes, or write the equation of a transformed function from a described change. According to the IB, transformations sit within Topic 2 (Functions) in the current Analysis & Approaches and Applications & Interpretation guides, first examined in 2021.

Both. Transformations sit in the SL core of Topic 2, so every AA and AI student meets them, whether SL or HL. HL students go further — applying transformations to a wider range of functions, including composite and inverse functions, and combining several transformations in one question.

Not usually — most transformation questions test whether you understand the rule, not whether you can graph on a calculator. Paper 1 (no GDC) regularly includes sketch-and-label transformation questions, while Paper 2 might ask you to use your GDC to check a transformed graph's key features.

Learn them as a table, not a list — group by what changes (inside vs outside the function) and test yourself on one coordinate at a time. Most students who lose marks here haven't practised enough varied examples, not because they don't know the rule in theory.

The biggest one: assuming horizontal shifts move in the same direction as the sign inside the bracket. $f(x+2)$ moves left, not right — students consistently get this backwards under exam pressure. The second: forgetting that a stretch factor between 0 and 1 compresses the graph, not stretches it.

Sketch the original function first, mark its key features (intercepts, turning points, asymptotes), then apply each transformation in the correct order — stretches and reflections before translations, unless the question states otherwise. Label the new coordinates of at least two key points on your final sketch.

Neither route makes the core rules harder — they're identical in both subjects. AA tends to test transformations more abstractly, often combined with algebraic proof or composite functions, while AI leans towards graphical, GDC-supported, real-world modelling contexts like population or temperature curves.

The underlying rules are near-identical to A-level Core Maths, but IB tests transformations more synoptically — combined with trig identities, composite functions or modelling contexts rather than in isolation. Students coming from an A-level background usually recognise the rules quickly but need practice applying them within IB's more integrated question style.

Look for resources with worked past-paper style questions on transformations specifically, not just general function topics — that's where most students actually lose marks. Topical worksheets that isolate this skill, paired with full mock papers to test it under time pressure, work better than general revision guides alone.