Graphs and Transformations summary

Key learning points

• $y=f(x)+a$ shifts up; $y=f(x-a)$ shifts right.
• Vertical stretch $y=af(x)$; horizontal stretch $y=f(ax)$ by factor $1/a$.
• Reflections: $y=-f(x)$ in the $x$-axis; $y=f(-x)$ in the $y$-axis.
• Track intercepts and asymptotes after each transformation.

Worked example 1 — Gradient

Through $(1,2)$ and $(3,8)$. Gradient?

Working

Rise over run.

Worked example 2 — Y-intercept

$y=3x-4$ meets the $y$-axis where?

Working

Set $x=0$.

Worked example 3 — Evaluate

For $y=2x+1$, find $y$ when $x=3$.

Working

Substitute.

Worked example 4 — Describe

How does $y=(x-2)^2+3$ relate to $y=x^2$?

Working

Inside the function affects $x$ with the opposite sign.

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.