Rational and Radical Functions

Lesson 4

Math

Unit 4

11th Grade

Lesson 4 of 18

Objective


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

Common Core Standards


Core Standards

  • N.RN.A.2 — Rewrite expressions involving radicals and rational exponents using the properties of exponents.
  • F.IF.B.5 — Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. Modeling is best interpreted not as a collection of isolated topics but in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.

Foundational Standards

  • F.IF.A.1

Criteria for Success


  1. Convert rational exponents to radicals and radicals to rational exponents, including negative rational exponents. 
  2. Define a function with a stated domain. 
  3. Describe how the domain restriction for a radical expression impacts the domain of a rational function. 
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Anchor Problems


Problem 1

Graph the following equation: $${f(x)={1\over{\sqrt{x}}} }$$

Guiding Questions

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Problem 2

What is the domain for the following function? 

$${g(x)=x^{3\over2}}$$

Guiding Questions

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Problem 3

Write a function that has a negative rational exponent with a domain of $${x>2.}$$ 

Guiding Questions

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Target Task


Find the domain for the following function. Explain your reasoning. 

$${h(x)=(2x-4)^{-2\over3}(x+3)^{1\over2}}$$

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 first rewrite the expression (as in the target task) and then identify the domain. 
  • Include problems where students need to find and correct a mistake or complete a problem that has been started. 
  • Include problems that review rewriting rational exponents as radicals. Include examples that are algebraic and numeric. 
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Lesson 3

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Lesson 5

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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