Exam Strategy

Readiness Check

• Factor num and den; list real denominator zeros.
• Check whether each is also a numerator zero; compare multiplicities if shared.
• Conclude VA vs not (hole preview).
• Write one-sided limits near a VA.

Before the Exam

1. Drill: den zero only → VA. 2. Drill: shared factor with den mult > num mult → still VA. 3. Drill: equal mult after cancel → not VA (hole later). 4. Practice $\lim_{x\to a^\pm}$ language.

During Multiple Choice

• Factor first; don’t guess from the unfactored constant term.
• Shared factor ≠ automatic “no VA.”
• HA answers are wrong for “near $x=a$” blow-up questions.

During Free Response

1. State domain candidates from $q(x)=0$. 2. For each $a$, compare presence/multiplicities in $p$ and $q$. 3. List VA equation(s) $x=a$. 4. Describe nearby unbounded behavior with one-sided limits.

Common Traps

• Calling canceled factors VAs.
• Describing VA with $y\to b$ (that’s horizontal).
• Forgetting left vs right sides can go to opposite infinities.

60-Second Checklist

• Den zeros listed?
• Num check / multiplicity compare?
• VA equations correct?
• One-sided limits if asked?