Rational and Radical Functions

Lesson 13

Math

Unit 4

11th Grade

Lesson 13 of 18

Objective


Describe transformations of rational functions.

Common Core Standards


Core Standards

  • F.BF.B.3 — Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
  • F.IF.C.7.D — Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.

Foundational Standards

  • F.BF.B.3

Criteria for Success


  1. Given the transformational form of a rational equation, identify the transformations that have occurred. 
  2. Describe how the features of a rational function are transformed when the function is transformed. 
  3. Apply the knowledge of how features are transformed to use asymptotes, intercepts, and sign charts to identify transformations without algebraic manipulation into the transformational form. 
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Anchor Problems

25-30 minutes


Problem 1

Given the graph shown below of $${a+{b\over(x+c)}}$$, where $${b=1}$$, $${c=0}$$, and $${a=0 }$$

 

Use this Desmos graph to describe the effect that changing the values of $$a$$, $$b$$, and $$c$$ has on the location of the graph. 

 

Guiding Questions

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Problem 2

Graph the function $${g(x)={x+2\over{{x-}3}}}$$ using asymptote(s), $${x-}$$ and $${y-}$$intercepts, and a sign chart. 

What transformations have occurred from the parent function of $${1\over{x}}$$

Guiding Questions

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References

EngageNY Mathematics Precalculus and Advanced Topics > Module 3 > Topic B > Lesson 15Example 1

Precalculus and Advanced Topics > Module 3 > Topic B > Lesson 15 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..

Target Task

5-10 minutes


Below is an equation and the graph of the function $${g(x)}$$. 

 

$${g(x)}={3x-7\over{x-3}}$$

 

Describe the transformations that have occurred from the parent function of $${1\over{x}}$$. Write the equation of the rational function in the transformational form. 

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.

Next

Solve simple radical equations.

Lesson 14
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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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