Exam Strategy

Readiness Check

You are ready when you can (1) translate $f(x)+k$ and $f(x+h)$ with correct directions, (2) apply $a f(x)$ and $f(bx)$ including reflections, (3) map a point through a combo, and (4) update domain/range for common parents.

Prep Sequence

1. Drill direction of $f(x\pm h)$. 2. Drill $|a|$ and $1/|b|$ with sign checks. 3. Three combo point maps. 4. Domain/range for $\sqrt{x-h}$, $a|x|+k$, $1/(x-h)$. 5. Description → equation matching.

On the Exam

• Underline inside vs outside pieces before writing the story.
• For $f(x+h)$, shift by $-h$ (opposite the sign you see with $x$).
• For $f(bx)$, new $x$-coordinates are old ones divided by $b$.
• State domain/range only after all transformations are listed.

Common Traps

• Horizontal shift direction reversed.
• Confusing vertical factor $a$ with horizontal factor $b$.
• Skipping reflection language for negative coefficients.
• Leaving parent domain after a horizontal move.

Quick Checklist

• [ ] Inside vs outside identified
• [ ] Horizontal direction = opposite of $h$ in $f(x+h)$
• [ ] Dilations use $|a|$ and $1/|b|$ with reflection notes
• [ ] Point map checked
• [ ] Domain/range updated if needed