What Is a Piecewise Linear Function?

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From a geometric point of view, Figure 16.1 shows a conventional piecewise linear function f(x). This particular function consists of four segments. If you consider the function over four separate intervals, (-, 4) and [4, 5) and [5, 7) and [7, ), you see that f(x) is linear in each of those separate intervals. For that reason, it is said to be piecewise linear. Within each of those segments, the slope of the linear function is clearly increasing or decreasing. The points where the slope of the function changes are known as breakpoints. The piecewise linear function in Figure 16.1 has three breakpoints.