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Piecewise-Defined Functions

A piecewise fucntion exists when a function is defined by two or more different functions throughout its domain. The first step in evaluating a piecewise function is to determine which function definition applies depending on the value of x that is being input. Once that has been determined, we evaluate the function as usual by substituting  in the given value of x.


Piecewise Function Example

Absolute Value Functions

An absolute value function can be rewritten as a piecewise function. Absolute value is the distance from a number 'x' to 0 on the real number line. Therefore, when the value of a function is equal to zero or is positive, taking its absolute value doesn't change it; however, if the value is negative, taking absolute value changes the sign. Therefore, the definition of the function changes depending on whether or not x ≥ 0.

Piecewise Function Example

Example 1:

Example 2:

Example 3: