Exam Strategy
Readiness Check
- Factor; find shared real zeros.
- Compare multiplicities: num ≥ den ⇒ hole; den > num ⇒ VA.
- Find $L=\lim_{x\to c}r(x)$ for hole coordinates $(c,L)$.
- State that $r(c)$ is still undefined.
Before the Exam
1. Drill equal-multiplicity cancel → hole; evaluate simplified form. 2. Drill num mult > den mult → hole; leftover num factor may affect $L$. 3. Drill den mult > num mult → VA (not hole). 4. Practice writing $\lim_{x\to c}r(x)=L$.
During Multiple Choice
- Shared factor ≠ automatic hole—check multiplicities.
- Hole points need both coordinates when asked.
- “Undefined but limit finite” = hole language.
During Free Response
1. Factor and list shared zeros with multiplicities. 2. Classify hole vs VA for each. 3. For each hole: simplify, compute $L$, report $(c,L)$. 4. Emphasize domain: still exclude $c$.
Common Traps
- Calling a hole a VA.
- Reporting only $x=c$ without $L$.
- Thinking the hole is an $x$-intercept automatically ($L$ might be 0, but that still isn’t “$r(c)=0$”).
- Forgetting leftover factors after partial cancel.
60-Second Checklist
- Multiplicities compared?
- Hole vs VA correct?
- Point $(c,L)$ found?
- Still undefined at $c$?