Precalculus: Finding Extraneous Solutions

In this activity, students will graphically solve a radical equation. They are given each step of solving the equation. For each step students are to graph each side of the equation as a separate function and find the intersection. Students will determine in which step the extraneous solution appears.

Then students will confirm the real and extraneous solutions using a table of values and the Home screen. When students set the functions back to the original equation, they will see that one x-value gives a result of 0 or false and the other gives a result of 1 or true. In the extension, students can work to determine when the extraneous solution appears for a rational equation.