Unit 04 · 3 Weeks · 8 Lessons
Rational Expressions, Equations & Functions
How do excluded values, asymptotes, holes, and rates of change shape rational expressions and models?
Complete instructional sequence
Detailed Lessons
Lessons include objectives, formulas, concept development, worked examples, guided and independent practice, differentiated pathways, application, misconception analysis, mastery evidence, reflection, and local completion.
Simplifying Rational Expressions & Restrictions
Rational expressions simplify by factoring numerator and denominator and canceling common nonzero factors. Original denominator restrictions remain even after cancellation.
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Lesson 02Multiplying and Dividing Rational Expressions
Factoring before multiplication often exposes common factors and reduces work. Division means multiplying by the reciprocal of the divisor, with all original and reciprocal restrictions recorded.
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Lesson 03Adding and Subtracting Rational Expressions
Rational terms add only after they share a denominator. Factor denominators first, construct the least common denominator, and combine numerators carefully.
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Lesson 04Solving Rational Equations & Extraneous Solutions
Clearing denominators converts a rational equation to an algebraic equation, but candidate solutions must be checked against the original equation and its restrictions.
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Lesson 05Reciprocal Functions, Asymptotes & Holes
A rational graph’s domain, intercepts, holes, vertical asymptotes, and end behavior come from its factored structure. Horizontal or slant asymptotes describe long-run behavior, not forbidden lines.
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Lesson 06Transformations and Features of Rational Functions
Transformed reciprocal functions use h and k to locate asymptotes and a/b to control orientation and scale. Feature analysis should be tied to the original equation.
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Lesson 07Direct, Inverse, Joint & Combined Variation
Variation equations encode proportional structure. Determine k from known values, preserve units, and test whether the model form is reasonable.
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Lesson 08Rational Models, Rates & Work Problems
Rational models arise when rates, densities, resistances, or per-unit quantities combine. Define quantities and units before manipulating equations.
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Practice and evidence
Unit Resources
Foundation Practice
Prerequisite support, smaller steps, representation aids, and correction prompts.
Core Practice
Complete standards-level definitive-answer practice and explanation.
Extended Practice
Generalization, proof, parameter analysis, technology, and deeper modelling.
Unit Mastery Check
Fresh randomized questions with scoring and explanations.
Rational Function Design & Rate Model
Applied investigation with evidence, validation, limitations, and defense.
Family Guide
Plain-language overview, support questions, and evidence expectations.
Teacher Guide
Pacing, differentiation, assessment, misconceptions, and records.
Vocabulary Data
Core English terms with Spanish, French, Arabic, and Portuguese support.
Standards Map
Unit concepts and broad national/international alignment categories.