Topic summary · IGCSE handout

Transformations of Graphs summary

Graph transformations move $y=f(x)$ : translations, stretches and reflections using function notation.

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Key learning points

$y=f(x)+a$ up; $y=f(x-a)$ right; $y=af(x)$ vertical stretch; $y=f(ax)$ horizontal stretch by $1/a$ .
$y=-f(x)$ reflect in $x$ -axis; $y=f(-x)$ in $y$ -axis.
Apply combined transformations in a consistent order.

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.

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