A is called
increasing when as the
x-values increase, the values of
f(x) also
increase. On the other hand, a function is called
decreasing when, as
x increases,
f(x) decreases. An
increasing interval is an of the for an increasing function. A
decreasing interval is an interval of the independent variable for a decreasing function.
A point where a function has a is neither included in an increasing or a decreasing interval.
The previous applet shows a function that contains two increasing intervals and one decreasing interval. Each can be described in terms of the
x-values.
From left side to x=-2From x=-2 to x=0From x=0 to right side→→→IncreasingDecreasingIncreasing
Although the entire graph cannot be seen, it is reasonable to assume that it continues in the same manner. In that case, for all
x-values less than
x=-2, f will be increasing. For all
x-values greater than
x=0, f will also be increasing.
Increasing Intervals:-∞0Decreasing Interval:-2<x<-2<x<∞<x<0
A point where the function switches between decreasing and increasing is known as a .