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Unit: Module 3: Rational and exponential functions

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Topic A: Lesson 1: Solutions to polynomial equations

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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!

Topic A: Lessons 2-3: Roots of complex numbers

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Powers of complex numbersGet 3 of 4 questions to level up!

Topic A: Lessons 4-5: The binomial theorem

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Expand binomialsGet 3 of 4 questions to level up!

Quiz 1

Level up on the above skills and collect up to 320 Mastery points

Topic A: Lessons 6-7: Ellipses

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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!

Quiz 2

Level up on the above skills and collect up to 480 Mastery points

Topic A: Lesson 8: Hyperbolas

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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!

Quiz 3

Level up on the above skills and collect up to 240 Mastery points

Topic A: Lesson 9: Volume and Cavalieri’s principle

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Lesson 9: No content yet
(Opens a modal)

Topic B: Lessons 10-11: Simplifying rational expressions

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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!

Quiz 4

Level up on the above skills and collect up to 240 Mastery points

Topic B: Lessons 10-11: Multiplying & dividing rational expressions

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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!

Quiz 5

Level up on the above skills and collect up to 240 Mastery points

Topic B: Lessons 10-11: Adding & subtracting rational expressions

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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!

Quiz 6

Level up on the above skills and collect up to 480 Mastery points

Topic B: Lessons 12-13: End behavior and asymptotes of rational functions

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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!

Topic B: Lessons 14-15: Graphing rational functions

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Graphs of rational functionsGet 3 of 4 questions to level up!

Quiz 7

Level up on the above skills and collect up to 320 Mastery points

Topic B: Lessons 16-17: Function composition

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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!

Quiz 8

Level up on the above skills and collect up to 320 Mastery points

Topic C: Lesson 18: Inverse functions

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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!

Quiz 9

Level up on the above skills and collect up to 160 Mastery points

Topic C: Lesson 19: Restricting the domain

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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!

Topic C: Lessons 20-21: Inverse relationship of exponentials and logarithms

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Relationship between exponentials & logarithmsGet 3 of 4 questions to level up!

Quiz 10

Level up on the above skills and collect up to 320 Mastery points

Up next for you:

Unit test

Level up on all the skills in this unit and collect up to 3900 Mastery points!

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