Curriculum  /  Math  /  11th Grade  /  Unit 4: Rational and Radical Functions  /  Lesson 10

Rational and Radical Functions

Lesson 10

Math

Unit 4

11th Grade

Lesson 10 of 18

Objective

Identify features of rational functions with a larger degree in the denominator than in the numerator. Describe how to calculate these features algebraically.

Common Core Standards

Core Standards

  • A.APR.D.6 — Rewrite simple rational expressions in different forms; write a(x /b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
  • F.IF.C.7.D — Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.

Foundational Standards

  • F.IF.B.4

Criteria for Success

  1. Describe horizontal and vertical asymptotes and identify their location on a graph of a rational function. 
  2. Describe how to calculate the vertical and horizontal asymptotes of rational functions algebraically.
  3. Describe how you know that the end behavior of functions with a larger degree in the denominator than in the numerator will approach zero. 
  4. Write a rational function with features of asymptotes, $${x- }$$and $${y-}$$intercepts, and end behavior described. 
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Anchor Problems

25-30 minutes

Problem 1

What do all of these functions have in common? 

$${j(x)={2x^2-2\over{x^3}}}$$

$${h(x)={x^2-2\over{x^4-81}}}$$

$${l(x)={3x+3\over{x^3-2x^2-3x}} }$$

 

Guiding Questions

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Problem 2

What are the $${x-}$$ and $${y-}$$intercepts and end behavior of the function $${h(x)}$$? 

Guiding Questions

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Target Task

5-10 minutes

Problem 1

A rational function has a horizontal asymptote of zero and a vertical asymptote of zero. 
What information can you determine about the equation of the rational function from this information? 

Problem 2

Below is a function. What are the vertical and horizontal asymptotes of the function? What is the end behavior of the function? 

 

$${g(x)={x+2\over{x^2}}}$$

 

$${h(x)={x^3+2\over{x^2}}}$$

Additional Practice

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

  • Include problems where students need to write a function that contains particular properties pertaining to the asymptotes, intercepts, and end behavior. 
  • Include problems that ask students to compare features and properties of different types of rational functions. 

Next

Identify features of rational functions with a larger degree in the numerator than in the denominator. Describe how to calculate these features algebraically.

Lesson 11
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Introduction to Rational and Radical Functions and Expressions

Topic B: Features of Rational Functions and Graphing Rational Functions

Topic C: Solve Rational and Radical Equations and Model with Rational Functions

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