Curriculum  /  Math  /  11th Grade  /  Unit 4: Rational and Radical Functions  /  Lesson 12

Rational and Radical Functions

Lesson 12

Math

Unit 4

11th Grade

Lesson 12 of 18

Objective

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.

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
  • F.IF.C.8

Criteria for Success

  1. Analyze the vertical asymptotes, horizontal asymptotes, removable discontinuities presented graphically for indications of numerator/denominator degree relationship, cancelled factors, leading signs, and coefficients. 
  2. Analyze the numerator/denominator degree relationship, cancelled factors, leading signs, and coefficients to identify graphical features associated with a rational function. 
  3. Use the features of a rational function presented graphically to create a possible rational equation. 
  4. Use a sign chart to graph an approximation of the rational function. 

Tips for Teachers

Sign charts are first taught in Algebra 2, Unit 3, Lesson 5. The following resource may be helpful to provide background knowledge on how to develop a sign chart for graphing functions.

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Anchor Problems

25-30 minutes

Problem 1

Graph the following rational function: 

 

$${f(x)={x^2-2x+1\over{x-1}}}$$

 

Guiding Questions

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Problem 2

Write an equation of a rational function that has asymptotes at $${x=-1}$$ and $${y=1}$$. Check your solution in your graphing calculator. 

Guiding Questions

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Problem 3

Graph $${x-1\over{x^2-x-6}}$$ using a sign chart to approximate the shape. 

Guiding Questions

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Target Task

5-10 minutes

Write a rational function that has a vertical asymptote at $${x=2}$$ and a removable discontinuity at $${ x=4}$$.

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 that require students to practice skills from the entire unit. 
  • Include problems where a graph is mismatched with an equation. Ask students to change the equation so that it is a better approximation of the graph. 
  • Include problems where students need to write an equation that models a graph shown or properties provided. 

Next

Describe transformations of rational functions.

Lesson 13
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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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