Study Guide
Learning Objectives
- Describe polynomial end behavior as $x\to\infty$ and $x\to-\infty$ with limit notation.
- Explain leading-term dominance for large $|x|$.
- Determine end behavior from degree parity and leading-coefficient sign.
- Match equations, graphs, and verbal “left/right” descriptions.
Suggested Practice Sequence
1. Four cases with $\pm x^2$, $\pm x^3$. 2. Identify leading term in scrambled polynomials. 3. Write formal limits from equations. 4. Match graphs to limit pairs. 5. Dominance explanations in FRQ sentences. 6. Link to 1.4: even degree global max/min vs unbounded ends.
Classroom / Check-In Moves
- Require both limits on every item.
- Cold-call: “What dominates for large $|x|$?”
- Sort card sort: equations → end-behavior case.
Misconception Watch-List
- End behavior depends on all terms equally.
- A local max means the right end goes down.
- Odd degree always rises both ways.
Vocabulary to Own
- end behavior
- leading term / leading coefficient
- dominate (for large $|x|$)
- $\lim_{x\to\infty}$, $\lim_{x\to-\infty}$
- unbounded increase/decrease
Materials Map
- Practice: identify leading term + write limits
- Word: long-run applied models
- Mixed / multi-*: graph match + 1.4/1.5 links
- Review & practice test: timed four-case fluency
- Interactive: quick checks