What is the that makes ? The answer is really simple or . In general if (this is important). The equation always has to solutions, namely . So the strategy of solving equation with absolute value is to bring the absolute value to the left hand side and the rest on the right hand side and then use the property that has solutions . Here is an example:

Solve .

Rewrite the equation as . Now think of the terms inside the absolute value as one single entity. Then using the property mentioned above this entity must be equal to 2 or -2, mathematically or and then  you can solve each of these equation.

The video playlist below will give you more examples on how to solve equation with absolute value.

A piecewise function is a function that is defined differently on different part of its domain. One of the most common function is the absolute value function. Absolute value function is defined as

This definition tells us that if your is non-negative () use the rule , otherwise use the rule .

In the video playslist below you will learn how to graph a piece wise function. You will also learn that given a graph of a piece wise function, how to construct the definition of the function itself and finally there is some tutorial how to graph a piecewise function on your calculator.