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# Unit 3: Module 3: Rational and exponential functions

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## About this unit

"Students revisit the fundamental theorem of algebra as they explore complex roots of polynomial functions. They use polynomial identities, the binomial theorem, and Pascal’s Triangle to find roots of polynomials and roots of unity. Students compare and create different representations of functions while studying function composition, graphing functions, and finding inverse functions." Eureka Math/EngageNY (c) 2015 GreatMinds.org### Learn

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- Factor polynomials: complex numbersGet 3 of 4 questions to level up!
- Zeros of polynomials (with factoring)Get 3 of 4 questions to level up!

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- Expand binomialsGet 3 of 4 questions to level up!

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- Graph & features of ellipsesGet 3 of 4 questions to level up!
- Center & radii of ellipses from equationGet 3 of 4 questions to level up!
- Ellipse standard equation & graphGet 3 of 4 questions to level up!
- Foci of an ellipse from radiiGet 3 of 4 questions to level up!
- Foci of an ellipse from equationGet 3 of 4 questions to level up!
- Equation of an ellipse from featuresGet 3 of 4 questions to level up!

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- Vertices & direction of a hyperbolaGet 3 of 4 questions to level up!
- Foci of a hyperbola from equationGet 3 of 4 questions to level up!
- Equation of a hyperbola from featuresGet 3 of 4 questions to level up!

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- Apply Cavalieri's principleGet 3 of 4 questions to level up!

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- Reduce rational expressions to lowest terms: Error analysisGet 3 of 4 questions to level up!
- Reduce rational expressions to lowest termsGet 3 of 4 questions to level up!
- Simplify rational expressions (advanced)Get 3 of 4 questions to level up!

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- Multiply & divide rational expressions: Error analysisGet 3 of 4 questions to level up!
- Multiply & divide rational expressionsGet 3 of 4 questions to level up!
- Multiply & divide rational expressions (advanced)Get 3 of 4 questions to level up!

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- Add & subtract rational expressions: like denominatorsGet 3 of 4 questions to level up!
- Add & subtract rational expressions (basic)Get 3 of 4 questions to level up!
- Least common multipleGet 3 of 4 questions to level up!
- Add & subtract rational expressions: factored denominatorsGet 3 of 4 questions to level up!
- Add & subtract rational expressionsGet 3 of 4 questions to level up!
- Nested fractionsGet 3 of 4 questions to level up!

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- End behavior of rational functionsGet 3 of 4 questions to level up!
- Rational functions: zeros, asymptotes, and undefined pointsGet 3 of 4 questions to level up!
- Analyze vertical asymptotes of rational functionsGet 3 of 4 questions to level up!

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- Graphs of rational functionsGet 3 of 4 questions to level up!
- Divide quadratics by linear expressions (with remainders)Get 3 of 4 questions to level up!

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- Evaluate composite functionsGet 3 of 4 questions to level up!
- Evaluate composite functions: graphs & tablesGet 3 of 4 questions to level up!
- Find composite functionsGet 3 of 4 questions to level up!
- Model with composite functionsGet 3 of 4 questions to level up!

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- Evaluate inverse functionsGet 3 of 4 questions to level up!
- Finding inverses of linear functionsGet 3 of 4 questions to level up!

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- Verify inverse functionsGet 3 of 4 questions to level up!
- Determine if a function is invertibleGet 3 of 4 questions to level up!
- Restrict domains of functions to make them invertibleGet 3 of 4 questions to level up!

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- Relationship between exponentials & logarithmsGet 3 of 4 questions to level up!
- Exponential model word problemsGet 3 of 4 questions to level up!

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