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Study Guide

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Learning Objectives

  • Describe rational end behavior via quotient of leading terms.
  • Classify dominance: numerator, denominator, or neither.
  • Locate horizontal asymptotes ($y=0$ or $y=a_n/b_m$) or recognize slant / no HA.
  • Use limit notation for HA $y=b$.

Suggested Practice Sequence

1. Denominator-dominates → $y=0$ with limits. 2. Equal degrees → ratio HA. 3. Numerator dominates by 1 → slant awareness. 4. Numerator dominates by 2+ → polynomial-like ends (link 1.6). 5. Mixed identification from equations. 6. FRQ write-ups with dominance language.

Classroom / Check-In Moves

  • Require a “who dominates?” sentence before the HA answer.
  • Sort functions into three HA buckets + slant bucket.
  • Cold-call limit sentences for $y=b$.

Misconception Watch-List

  • HA is always $y=0$.
  • HA is the $y$-intercept.
  • End behavior = vertical asymptotes.

Vocabulary to Own

  • rational function
  • dominate / quotient of leading terms
  • horizontal asymptote
  • slant (oblique) asymptote
  • $\lim_{x\to\pm\infty}r(x)=b$

Materials Map

  • Practice: degree compare + HA/slant
  • Word: long-run applied rational models
  • Mixed / multi-*: link to polynomial ends (1.6)
  • Review & practice test: timed classification
  • Interactive: quick checks

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