Exam Strategy
Readiness Check
You are ready when you can:
- State Dom $(0,\infty)$ and Range $\mathbb{R}$.
- Describe increasing/decreasing and concavity.
- Write end-behavior limits and name VA $x=0$.
- Reject false extrema/inflection claims on the full domain.
On the AP Exam
- MCQ: Dom/Range, asymptote, monotonicity, end behavior.
- FRQ: describe key features from equation or graph.
- Skill focus: 3.A describe characteristics with appropriate precision.
Tactics
1. Always start with Dom $>0$ and VA $x=0$. 2. Use base $b$ and coefficient $a$ to decide increase/decrease and concavity direction. 3. Limits: for $b>1$, as $x\to 0^+$ log $\to -\infty$; as $x\to\infty$ log $\to\infty$ (signs flip for $0<b<1$ or negative $a$). 4. Say "always mono / always one concavity" like exponential inverses. 5. Closed interval: extrema can occur at endpoints only.
Common Traps
- Dom $=\mathbb{R}$.
- Horizontal asymptote at $y=0$.
- Inflection point on the graph.
- Mixing end-behavior directions for growth vs decay bases.
Quick Checklist
- [ ] Dom and Range
- [ ] VA $x=0$
- [ ] Mono + concavity
- [ ] Limits both ends
- [ ] No false extrema/inflection on Dom