Investigating a Radical Function

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Objective

Students will be able to investigate a single radical function, construct its graph, and have their first encounter with an extraneous solution to a radical equation.

Big Idea

A single radical function, carefully studied, leads students to important conclusions about inverse functions and extraneous solutions.

Lesson Author

Jacob Nazeck

Fort Collins, CO

Grade Level

Eleventh grade

Subjects

Math

Algebra

Function Operations and Inverses

radical equations

Standards

HSA-REI.A.2

Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

HSF-IF.C.7b

Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

MP1

Make sense of problems and persevere in solving them.

MP2

Reason abstractly and quantitatively.

MP3

Construct viable arguments and critique the reasoning of others.

MP7

Look for and make use of structure.

Lesson Beginning (Opener)

10 minutes

Engaging Students in Discussion

InvestigatingRadicalFunc_Opener_Narrative.docx page 1

The Investigation

25 minutes

First, I will hand out Investigating Radicals 1 and ask the students to begin working individually. This initial investigation is fairly mechanical, with student evaluating the given function and producing a graph. At this stage, I think it's very important that they make the graph by hand, so I will not allow graphing calculators yet.

As students finish the graph, and I've seen that it's correct, I'll hand out Investigating Radicals 2. This really brings us to the heart of the lesson since these questions will focus the students' attention on the limited domain and range of the function. As they begin solving radical equations, they will see extraneous solutions arise and they will be able to use their graph to identify them. In the next section, the students themselves will explain the how and why of these features of radical functions.

Please see the video narrative for more details.