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Study Guide — Polynomial, rational, exponential, and logarithmic families

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Pre-calculus · Honors

Honors-depth study guide for Polynomial, rational, exponential, and logarithmic families.

What this standard means

  • Analyze end behavior and zeros of polynomials
  • Graph rational functions with asymptotes
  • Compare growth rates of function families
  • Transform parent functions

_See printable PDF for diagram._

How to use the 20 practice sets

| Sets | When to use | | --- | --- | | 1–5 | Intro — explore together, short written items | | 6–10 | Core skills — diagrams and written practice | | 11–15 | Mixed review — explain thinking | | 16–20 | Stretch — word problems and mastery tasks |

Pacing: 10–15 minutes per session.

How to practice

1. Sketch graphs from key points 2. Use function notation consistently 3. Identify intercepts, maxima, and intervals

_See printable PDF for diagram._

Common mistakes

  • Confusing x and y in notation
  • Misreading graph scales

Review and practice tests

1. Start Review 1/10 when sets 1–3 feel comfortable. 2. Move up one review level with little help. 3. Use Practice Test 4/10–6/10 for mid-standard checks. 4. Practice Test 10/10 is the mastery bar for Polynomial, rational, exponential, and logarithmic families.

  • [ ] Evaluates functions in notation
  • [ ] Identifies domain, range, and key features
  • [ ] Interprets graphs in context

Materials for this standard

  • Practice Problems — 20 printable sets
  • Review — 10 difficulty levels
  • Practice Test — 10 difficulty levels
  • Answer key — for parents and tutors

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