In mathematics, functions are often described by an algebraic expression, like *f*(*x*) = *x*^{2} + 1. Sometimes, on the other hand, they’re **tabulated,** that is, the values for each possible argument are listed, as in

A third, and very common, way to describe a function is to give its values at particular points and tell how to *interpolate* between these known values. For instance, we might plot the temperature at noon and midnight of each day of a week; such a plot consists of 15 distinct dots (see Figure 9.1). But we could also make a guess about the temperatures at times between each of these, saying, for ...

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