Unformatted text preview: − despite the
fact that j (−1) = −j (1), j turned out not to be odd. Secondly, while the calculator may suggest
mathematical truths, it is the algebra which proves mathematical truths.5 1.7.1 General Function Behavior The last topic we wish to address in this section is general function behavior. As you shall see in
the next several chapters, each family of functions has its own unique attributes and we will study
them all in great detail. The purpose of this section’s discussion, then, is to lay the foundation for
that further study by investigating aspects of function behavior which apply to all functions. To
start, we will examine the concepts of increasing, decreasing, and constant. Before deﬁning
the concepts algebraically, it is instructive to ﬁrst look at them graphically. Consider the graph of
the function f given on the next page.
Reading from left to right, the graph ‘starts’ at the point (−4, −3) and ‘ends’ at the point (6, 5.5). If
we imagine walking from left to right on the graph, betw...
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