Mathematical Analysis (Honors)
Unit 5: Rational Functions
In this unit, students apply their understanding of transformations to build rational functions. Students identify key features of functions, including domain, range, end behavior, local (relative) and/or absolute extrema, continuity, zeros, intercepts, symmetry, holes, asymptotes, and whether the function is even/odd. Students solve rational equations by hand, checking for extraneous solutions. Students solve rational inequalities by hand, checking for extraneous solutions. Students calculate limits of rational functions algebraically and estimate limits from graphs and tables of values. Students decompose a fraction with a factorable quadratic denominator and a linear or constant numerator.
Students will:
Build and interpret functions that model relationships between two quantities
PC.AF.A.1
Identify key features of functions, including domain, range, end behavior, local (relative) and/or absolute extrema, continuity, zeros, intercepts, symmetry, holes, asymptotes, and whether the function is even/odd. (Focus primarily on logarithmic, logistic, rational, step, and piecewisedefined functions.)
PC.AF.A.2
Model realworld data with functions. Justify why the model is most appropriate for the problem situation.
PC.AF.A.3
Calculate limits algebraically and estimate limits from graphs and tables of values.
Use functions to solve equations and inequalities
PC.AF.B.7
Solve equations and inequalities involving rational functions.
MA.RF.A.1
Decompose a fraction with a factorable quadratic denominator and a linear or constant numerator.
Build and interpret functions that model relationships between two quantities
PC.AF.A.1
Identify key features of functions, including domain, range, end behavior, local (relative) and/or absolute extrema, continuity, zeros, intercepts, symmetry, holes, asymptotes, and whether the function is even/odd. (Focus primarily on logarithmic, logistic, rational, step, and piecewisedefined functions.)
 Check for Understanding: Graph  Discontinuity
 Review/Rewind: Intro to Rational Expressions
 Enrichment Tasks: Graphing Rational Functions
PC.AF.A.2
Model realworld data with functions. Justify why the model is most appropriate for the problem situation.
 Check for Understanding: Direct and Inverse Variation
 Review/Rewind: Combined Rates  Direct and Inverse Variation
 Enrichment Tasks: Ideal Gas Law  The Canoe Trip
PC.AF.A.3
Calculate limits algebraically and estimate limits from graphs and tables of values.
 Check for Understanding: End Behavior  Vertical Asymptote  Twosided Limits
 Review/Rewind: Intro to Limits
Use functions to solve equations and inequalities
PC.AF.B.7
Solve equations and inequalities involving rational functions.
 Check for Understanding: Single Rational Expression  Single Rational Expression (advanced)  Two Rational Expressions
 Review/Rewind: Single Rational Expression  Solving Rational Equations  Two Rational Expressions
 Enrichment Tasks: An Extraneous Solution
MA.RF.A.1
Decompose a fraction with a factorable quadratic denominator and a linear or constant numerator.
 Check for Understanding: Partial Fraction Expansion
 Review/Rewind: Partial Fraction Expansion
What are some signs of student mastery?

Tools & Technology
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