Properties of Functions
Increasing and Decreasing Functions
Def. A function is increasing in an interval P if P is contained in the domain of f(x) and for every x1 and x2 in P such that:
x1 < x2
we have:
f(x1) < f(x2)
Def. A function is decreasing in an interval P if P is contained in the domain of f(x) and for every x1 and x2 in P such that:
x1 < x2
we have:
f(x1) > f(x2)
In other words, a function is increasing if and only if its graph y=f(x) is climbing as x increases. A function is decreasing if and only if its graph y=f(x) is falling as x increases.
The first of the graphs below represents an increasing function on the interval depicted. The second graph represents a decreasing function.
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