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Unformatted text preview: ecause we are unable to fulﬁll the requirements of the deﬁnition 1.7 Graphs of Functions 75 for a local minimum, we cannot claim that f has one at (−4, −3). The point (4, −3) fails for
the same reason − no open interval around x = 4 stays within the domain of f .
13. The maximum value of f is the largest y -coordinate which is 3.
14. The minimum value of f is the smallest y -coordinate which is −3.
15. The graph appears to be symmetric about the y -axis. This suggests13 that f is even.
With few exceptions, we will not develop techniques in College Algebra which allow us to determine
the intervals on which a function is increasing, decreasing or constant or to ﬁnd the local maximums
and local minimums analytically; this is the business of Calculus.14 When we have need to ﬁnd such
beasts, we will resort to the calculator. Most graphing calculators have ‘Minimum’ and ‘Maximum’
features which can be used to approximate these values, as demonstrated below.
. Use a graphing calculator to approximate the intervals...
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