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Increasing Decreasing Intervals
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Increasing and Decreasing Intervals

A function 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 interval of the independent variable 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 maximum or a minimum 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.
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.
A point where the function switches between decreasing and increasing is known as a turning point.