1. Table of Contents Functions: Intervals of Increasing, Decreasing, Constant A function, f(x), is increasing on an open interval if for every x 1 > x 2 in the interval, f(x 1 ) > f(x 2 ). a x 2 x 1 b f(x1)f(x2)f(x1)f(x2) The graph illustrates this definition. In the interval (a, b), note x 1 > x 2. Also note f(x 1 ) > f(x 2 ). The end result is that in the interval (a, b), the graph moves uphill from left to right.

2. Table of Contents Functions: Intervals of Increasing, Decreasing, Constant Slide 2 A function, f(x), is decreasing on an open interval if for every x 1 > x 2 in the interval, f(x 1 ) < f(x 2 ). The graph illustrates this definition. In the interval (a, b), note x 1 > x 2. Also note f(x 1 ) < f(x 2 ). The end result is that in the interval (a, b), the graph moves downhill from left to right. a x 2 x 1 b f(x2)f(x1)f(x2)f(x1)

3. Table of Contents Functions: Intervals of Increasing, Decreasing, Constant Slide 3 a x 2 x 1 b f(x 1 ) = f(x 2 ) A function, f(x), is constant on an open interval if for every x 1  x 2 in the interval, f(x 1 ) = f(x 2 ). The graph illustrates this definition. In the interval (a, b), note x 1  x 2. Also note f(x 1 ) = f(x 2 ). The end result is that in the interval (a, b), the graph remains level.

4. Table of Contents Functions: Intervals of Increasing, Decreasing, Constant Slide 4 Example:State the open intervals on which the function shown graphed is increasing, decreasing, and constant. 1 2 3 4 5 6 7 5 4 3 2 15 4 3 2 1 The function is increasing on (- , 3). The function is decreasing on ( 5,  ). The function is constant on (3, 5).

5. Table of Contents Functions: Intervals of Increasing, Decreasing, Constant