What Is a Piecewise Linear Function?

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From a geometric point of view, Figure 18.1 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 constant, though it is different between segments. The points where the slope of the function changes are known as breakpoints. The piecewise linear function in Figure 18.1 has three breakpoints.