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

Rational and Radical Functions

Lesson 11

Math

Unit 4

11th Grade

Lesson 11 of 18

Objective

Identify features of rational functions with a larger degree in the numerator than in the denominator. 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 should you do to turn this function into a proper rational function? 

 

$${f(x)={x^3-4x\over{x^2}}}$$

 

Guiding Questions

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Problem 2

How are the horizontal and vertical asymptotes different or similar in each of the following functions? Compare both algebraically and graphically. 

 

$${f(x)={x^3-4\over{x^4}}}$$

 

$${g(x)={x^3-4\over{x^3}}}$$

 

$${h(x)={x^3-4\over{x^2}}}$$

 

Guiding Questions

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Target Task

5-10 minutes

Consider the function:

 

$${f(x)={x^2-5x-6\over{-2x+5}}}$$

 

  1. State the domain
  2. Identify the horizontal and vertical asymptote(s), if applicable. 
  3. What is the end behavior? 

References

EngageNY Mathematics Precalculus and Advanced Topics > Module 3 > Topic B > Lesson 13 — Exit Ticket

Precalculus and Advanced Topics > Module 3 > Topic B > Lesson 13 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

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 use TI-84 skills to solve problems through graphical analysis and use of tables. 
  • Include problems that review all rational function concepts covered thus far in the unit, as well as some basic quadratic skills of factoring. 
  • Include problems such as “given vertical asymptote, horizontal asymptote, and domain, what else do you know about the function?”

Next

Analyze the graph and equations of rational functions and identify features. Use features of a rational function to identify and construct appropriate equations and graphs.

Lesson 12
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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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