Unformatted text preview: we do not mention the actual y values that f attains along the way. Thus, we report
where the behavior occurs, not to what extent the behavior occurs.6 Also notice that we do not
say that a function is increasing, decreasing or constant at a single x value. In fact, we would run
5
6 Or, in other words, don’t rely too heavily on the machine!
The notions of how quickly or how slowly a function increases or decreases are explored in Calculus. 1.7 Graphs of Functions 71 into serious trouble in our previous example if we tried to do so because x = −2 is contained in an
interval on which f was increasing and one on which it is decreasing. (There’s more on this issue
and many others in the exercises.)
y
7 (−2, 4.5) (6, 5.5) 6
5
4
3
2
1 −4 −3 −2 −1
−1 1 2 3 4 5 6 7 x −2
−3 (−4, −3) −4
−5 (4, −6) −6 (5, −6) −7
−8
−9 (3, −8) The graph of y = f (x)
We’re now ready for the more formal algebraic deﬁnitions of what it means for a function to be
increasing, decreasing or constant.
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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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