Unit 3: Rational Functions and Equations

Students transition from polynomials to rational functions and equations, analyzing asymptotic behavior, solving rational equations (including identifying extraneous solutions), proving polynomial identities, and deriving the finite geometric series sum formula.

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Unit

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Concept

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Practice

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Set 1

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Set 2

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Advanced

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Set 2

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What this unit covers

A Rational Functions · 4 lessons

Goals

• Identify asymptotes of rational functions from their equations.
• Interpret rational functions in context.

Lessons

1. Minimizing Surface Area
2. Graphs of Rational Functions (Part 1)
3. Graphs of Rational Functions (Part 2)
4. End Behavior of Rational Functions

B Rational Equations · 3 lessons

Goals

• Create simple equations involving a rational expression to solve problems.
• Solve equations involving rational expressions, and identify any extraneous solutions.

Lessons

1. Rational Equations (Part 1)
2. Rational Equations (Part 2)
3. Solving Rational Equations

C Polynomial Identities · 4 lessons

Goals

• Prove identities.
• Use the formula for the sum of the first n terms in a geometric sequence to solve problems.

Lessons

1. Polynomial Identities (Part 1)
2. Polynomial Identities (Part 2)
3. Summing Up
4. Using the Sum