5 at x 6 in this case we say the maximum11 of f is 55

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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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