Graphs and Transformations Topic Review summary

Key learning points

• Know shapes of $x^2$, $x^3$, $\frac{1}{x}$, $\sqrt{x}$, $|x|$, and simple trig/exp graphs.
• Translations, stretches, and reflections follow standard rules.
• Intercepts: set $x=0$ or $y=0$; asymptotes for reciprocal/exp/log graphs.
• Transform key points rather than redrawing from scratch.
• Describe transformations in full sentences for exam credit.

Worked example 1 — Asymptotes

Asymptotes of $y=\frac{1}{x-2}+3$.

Working

Translated reciprocal.

Worked example 2 — Transform

$y=f(x)+2$ relative to $y=f(x)$.

Working

Vertical shift.

Worked example 3 — Know shapes of x^2, x^3, \1{x}, \x, |x|, a

Know shapes of $x^2$, $x^3$, $\\frac{1}{x}$, $\\sqrt{x}$, $|x|$, and simple trig/exp graphs.

Working

Attempt without notes, then check the answers PDF.

Worked example 4 — Translations, stretches, and reflections f

Apply this idea from the Topic Review: Translations, stretches, and reflections follow standard rules.

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.