Investigating a Radical Function
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.
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The Investigation
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.
