A function is said to be increasing when, as the x-values increase, the values of f(x) also increase. On the other hand, the function is considered decreasing when, as x increases, f(x) decreases. An increasing interval is an interval of the independent variable where the function is increasing. A decreasing interval is an interval of the independent variable when the function is decreasing. Any points where a function has a maximum or a minimum are not included in either 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=- 2 & → && Increasing From x=- 2 to x=0 & → && Decreasing From x=0 to right side & → && Increasing 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: - ∞ &< x < - 2 [0.8em] 0 &< x < ∞ [0.8em] Decreasing Interval: - 2 &< x < 0 The point where a function switches between decreasing and increasing is known as a turning point.