Study Guide
Learning Objectives
- Construct additive and/or multiplicative transformations of a given function (1.12.A).
- Describe vertical translations $g(x)=f(x)+k$ and horizontal translations $g(x)=f(x+h)$ (shift by $-h$).
- Describe vertical dilations $g(x)=a f(x)$ and horizontal dilations $g(x)=f(bx)$, including reflections when $a<0$ or $b<0$.
- Combine transformations and state the sequence of geometric effects.
- Compare domain and range of a transformed function to its parent (1.12.A.6).
Suggested Practice Sequence
1. Pure vertical and horizontal translations; map points. 2. Pure vertical/horizontal dilations; reflections. 3. Two-step combos; order of operations on a point. 4. Domain/range shifts for $\sqrt{x}$, $|x|$, $1/x$, quadratics. 5. Build $g$ from a verbal description. 6. Mixed FRQ: equation ↔ description ↔ graph language.
Classroom / Check-In Moves
- Color-code “inside vs outside.”
- Cold-call the horizontal direction rule every day for a week.
- Require a point map for every combo before the verbal story.
Misconception Watch-List
- $f(x+3)$ means “right 3.”
- $f(2x)$ stretches horizontally by 2.
- Reflections forgotten when coefficients are negative.
- Domain unchanged after horizontal shifts of $\sqrt{x}$ or $1/x$.
Vocabulary to Own
- additive / multiplicative transformation
- vertical / horizontal translation
- vertical / horizontal dilation (stretch/compress)
- reflection over $x$-axis / $y$-axis
- parent function; domain; range
Materials Map
- Practice: name, build, map points
- Word: applied shift/stretch stories
- Mixed / multi-*: connect to parents from Unit 1
- Review & practice test: timed fluency
- Interactive: quick checks