Exam Strategy

Readiness Check

• Identify degrees and leading coefficients of numerator and denominator.
• Classify: den dominates / equal / num dominates (incl. slant).
• Write HA $y=b$ or state none; write matching limits when HA exists.
• Explain using quotient of leading terms / dominance.

Before the Exam

1. Drill three equal-degree examples with different leading-coefficient ratios. 2. Drill den-degree-higher → $y=0$. 3. Drill num = den+1 → recognize slant (division idea at a high level). 4. Practice limit sentences for HA $y=b$.

During Multiple Choice

• Compare degrees before expanding everything.
• Equal degree → $a_n/b_m$, not “always 1.”
• Vertical asymptote clues are not end-behavior answers.

During Free Response

1. State deg(num), deg(den), leading coefficients. 2. Name which polynomial dominates (or neither). 3. Conclude HA / slant / polynomial-like ends. 4. If HA $y=b$, write both-sided limit language as required.

Common Traps

• Canceling factors then forgetting end behavior still follows degrees of the simplified form for large $|x|$ (still OK to use leading terms of original when degrees unchanged by cancellation of lower terms—careful with holes later).
• Using $y$-intercept as HA.
• Saying “no asymptote” when $y=0$ is the HA.

60-Second Checklist

• Degrees compared?
• Leading-term quotient stated?
• HA / slant / none correct?
• Limits if HA?