Lesson 3

Lesson 3 Summary

 

Dmytro Bezsmertnyy, www.hidden-3d.com

 

In this lesson you investigated the following questions:

• How can the roots of absolute value equations be determined?
  
  
• Why are extraneous roots obtained sometimes when absolute value equations are solved algebraically?

In this lesson you learned graphical and algebraic strategies for solving absolute value equations. Since absolute value expressions are dependent on the sign of the expression contained in the absolute value symbol, there are two cases to consider when solving absolute value equations algebraically.

 

For the equation , where A is a mathematical expression, you must determine the solutions to the following two cases:

• Case 1: f(x) = A
  
  
• Case 2: −f(x) = A

You also learned that the algebraic method may yield extraneous roots. It is necessary, therefore, to verify that the roots either satisfy the specific domain or result in a true statement when substituted back into the original equation. Extraneous roots are obtained because the domain of each case is restricted to positive or negative values of x, but values outside of the domain emerge when solving quadratic and linear equations.

 

In the final lesson of this module you will explore reciprocal functions. These and absolute value functions may be used to develop further math concepts in subsequent math courses.