Transformations of Graphs summary

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

Outside addition is vertical.

Worked example 2 — Horizontal shift

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

Working

Inside minus shifts right.

Worked example 3 — Reflection

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

Working

Negate outputs.

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.