Answer
A piecewise defined function has different rules for different intervals of x.
Example: $f(x)=|x|=\left\{\begin{array}{ll}
-x & ,x < 0\\
x & ,x \geq 0
\end{array}\right.$
Work Step by Step
When we determine the value of f(x) in different ways,
depending on different intervals that x belongs to, we define it piecewise.
For each interval, a different rule.
An example is the$ $ absolute value function.
When x is negative, we change its sign,
and when x is nonnegative, we leave it as it is:
$f(x)=|x|=\left\{\begin{array}{ll}
-x & ,x < 0\\
x & ,x \geq 0
\end{array}\right.$
