Transformations of Graphs Topic Review summary

Key learning points

• $y=f(x)+a$ translates vertically; $y=f(x-a)$ translates horizontally.
• $y=af(x)$ stretches parallel to the $y$-axis; $y=f(ax)$ stretches parallel to the $x$-axis.
• $y=-f(x)$ reflects in the $x$-axis; $y=f(-x)$ reflects in the $y$-axis.
• Combine transformations in a clear order; track key points.
• $y=|f(x)|$ reflects negative parts above the $x$-axis.

Worked example 1 — Translate

$y=(x-2)^2+3$ vs $y=x^2$.

Working

Right 2, up 3.

Worked example 2 — Stretch

$y=f(2x)$ vs $y=f(x)$.

Working

Towards the $y$-axis.

Worked example 3 — y=f(x)+a translates vertically; y=f(x-a) t

$y=f(x)+a$ translates vertically; $y=f(x-a)$ translates horizontally.

Working

Attempt without notes, then check the answers PDF.

Worked example 4 — y=af(x) stretches parallel to the y-axis;

$y=af(x)$ stretches parallel to the $y$-axis; $y=f(ax)$ stretches parallel to the $x$-axis.

Working

Attempt without notes, then check the answers PDF.

Scaffolded Learning Sheet and answers (PDFs)

This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.