Topic summary · Pure advanced (P3)

Transformations of Graphs summary

Function transformations combine translations and stretches. Apply them consistently and track key points.

Open Learning Sheet — Transformations of Graphs Download Transformations of Graphs answers PDF

Files: P3-Transformations of Graphs.pdf · P3-Transformations of Graphs answers.pdf · free public downloads · diagrams in the PDFs

Key learning points

Horizontal changes alter the input; vertical changes alter the output.
$y=af(x)$ stretches vertically; $y=f(ax)$ stretches horizontally by $1/a$ .
Combined example: $y=2f(x-1)+3$ — right 1, ×2 vertical, up 3.
Asymptotes move with the graph.

Worked example 1 — Translation

Effect of $y=f(x)+3$ ?

Working

\text{up }3

Outside addition is vertical.

Worked example 2 — Horizontal shift

Effect of $y=f(x-2)$ ?

Working

\text{right }2

Inside minus shifts right.

Worked example 3 — Reflection

Effect of $y=-f(x)$ ?

Working

\text{reflect in }x\text{-axis}

Negate outputs.

Worked example 4 — Combined

Describe $y=f(2x)-4$ relative to $y=f(x)$ .

Working

\text{horizontal stretch scale }\tfrac{1}{2}\text{, then down 4}

The coefficient of $x$ compresses the graph horizontally.

Scaffolded Learning Sheet and answers (PDFs)

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Open Learning Sheet Answers PDF

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