College Algebra, 2013a

1.6 Graphs of Functions 101
on [−4, −2] 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. 7 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
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.)
We’re now ready for the more formal algebraic definitions of what it means for a function to be
increasing, decreasing or constant.
Definition 1.10. Suppose f is a function defined on an interval I. Wesayf is:
ˆ increasing on I if and only if f(a)