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Unformatted text preview: 1.8. Suppose f is a function deﬁned on an interval I . We say f is:
• increasing on I if and only if f (a) < f (b) for all real numbers a, b in I with a < b.
• decreasing on I if and only if f (a) > f (b) for all real numbers a, b in I with a < b.
• constant on I if and only if f (a) = f (b) for all real numbers a, b in I .
It is worth taking some time to see that the algebraic descriptions of increasing, decreasing, and
constant as stated in Deﬁnition 1.8 agree with our graphical descriptions given earlier. You should
look back through the examples and exercise sets in previous sections where graphs were given to
see if you can determine the intervals on which the functions are increasing, decreasing or constant.
Can you ﬁnd an example of a function for which none of the concepts in Deﬁnition 1.8 apply?
Now let’s turn our attention to a few of the points on the graph. Clearly the point (−2, 4.5) does
not have the largest y value of all of the points on the graph of f − indeed that honor goes to 72 Relations and Functions (6, 5.5) − but (−2, 4.5) sh...
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