Curriculum / Math / 11th Grade / Unit 4: Rational and Radical Functions / Lesson 15
Math
Unit 4
11th Grade
Lesson 15 of 18
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Solve radical equations and identify extraneous solutions.
The core standards covered in this lesson
A.REI.A.2 — Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
The foundational standards covered in this lesson
A.REI.A.1 — Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Solve the following equation:
$${\sqrt{-3x-5}-2=x+1}$$
$${(x-2)^{2\over3}=4}$$
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Below are three answers to the problem $${{{{\sqrt{x-2}=2-x}}}}$$. Which answer is correct? Explain your reasoning.
$${{{{\sqrt{x-2}=2-x}}}}$$
$${{x-2=4-4x+x^2}}$$
$${{0=6-5x+x^2}}$$
$${{x^2-5x+6=0}}$$
$${{(x-2)(x-3)=0}}$$
Solution: $${{x=2}}$$ and $${{x=3}}$$
$${x-2=4+x^2}$$
$${0=6-x+x^2}$$
$${x^2-x+6=0}$$
$${(x-3)(x+2)=0}$$
Solution: $${{x=3}}$$ and $${x=-2}$$
Solution: $${{x=2}}$$
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.
Lesson 14
Lesson 16
Topic A: Introduction to Rational and Radical Functions and Expressions
Define rational functions. Identify domain restrictions of rational functions.
A.APR.D.6 F.IF.B.5
Identify domain restrictions algebraically for non-invertible functions.
F.BF.B.4 F.IF.C.7.B
Graph and transform square root and cubic root functions.
F.BF.B.3 F.IF.C.7.B
Write rational functions in equivalent radical form and identify domain restrictions of rational and radical functions.
F.IF.B.5 N.RN.A.2
Write radical and rational exponent expressions in equivalent forms.
N.RN.A.2
Multiply and divide rational expressions and simplify using equivalent expressions.
A.APR.D.6 A.APR.D.7
Add and subtract rational expressions.
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Topic B: Features of Rational Functions and Graphing Rational Functions
Identify asymptotic discontinuities (also known as infinite discontinuities) and removable discontinuities in a rational function and describe why these discontinuities exist.
A.APR.D.6 F.IF.C.7.D
Identify features of rational functions with equal degrees in the numerator and the denominator. Describe how to calculate features of these types of rational functions algebraically.
Identify features of rational functions with a larger degree in the denominator than in the numerator. Describe how to calculate these features algebraically.
Identify features of rational functions with a larger degree in the numerator than in the denominator. Describe how to calculate these features algebraically.
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.
Describe transformations of rational functions.
F.BF.B.3 F.IF.C.7.D
Topic C: Solve Rational and Radical Equations and Model with Rational Functions
Solve simple radical equations.
A.REI.A.2
Solve rational equations.
A.APR.D.6 A.REI.A.2 A.REI.D.11
Write and solve rational functions for contextual situations.
A.APR.D.6 A.CED.A.2 N.Q.A.1
Analyze rational and radical functions in context and write rational functions for percent applications.
A.APR.D.6 A.CED.A.2 A.REI.A.2
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