Rational and Radical Functions

Lesson 3

Math

Unit 4

11th Grade

Lesson 3 of 18

Objective


Graph and transform square root and cubic root 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.B — Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

Foundational Standards

  • F.BF.B.4.A
  • A.CED.A.4

Criteria for Success


  1. Apply the standard function transformations to square root and cube root functions. 
  2. Describe how the domain restriction for a square root function is represented in the transformation of the function. 
  3. Identify the domain and range of square root and cube root functions represented by a graph or equation. 
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Anchor Problems

25-30 minutes


Problem 1

Below is a graph of a square root function. 

What is the equation that represents this function?

Guiding Questions

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Problem 2

Graph the following function on a coordinate plane: 

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

Guiding Questions

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Target Task

5-10 minutes


Problem 1

How would the graph of $$f(x)=\sqrt{x}$$ be affected if it were changed to $$g(x)=-2\sqrt{x}$$?

References

EngageNY Mathematics Algebra I > Module 4 > Topic C > Lesson 20

Algebra I > Module 4 > Topic C > Lesson 20 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..

Problem 2

Sketch and label the graphs of both $$f$$ and $$g$$

References

EngageNY Mathematics Algebra I > Module 4 > Topic C > Lesson 20

Algebra I > Module 4 > Topic C > Lesson 20 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..

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 identify the parent function and then guess as to how it was transformed. 
  • Include problems where students need to describe the domain and range of rational and radical functions. 
  • Include problems with roots other than 2. Focus on roots of 3 and 4. Be sure to ask about domain and range of these functions. 
  • Include problems where students review inverse functions and graph square and cube roots from their inverse functions. 

Next

Write rational functions in equivalent radical form and identify domain restrictions of rational and radical functions.

Lesson 4
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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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