Functions Intervals of Increasing Decreasing Constant A function

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). The graph illustrates this definition. In the interval (a, b), note x 1 > x 2. f(x 1) f(x 2) Also note f(x 1) > f(x 2). a x 2 x 1 b The end result is that in the interval (a, b), the graph moves uphill from left to right. Table of Contents

Functions: Intervals of Increasing, Decreasing, Constant 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. f(x 2) f(x 1) Also note f(x 1) < f(x 2). a x 2 x 1 b The end result is that in the interval (a, b), the graph moves downhill from left to right. Table of Contents Slide 2

Functions: Intervals of Increasing, Decreasing, Constant 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. f(x 1) = f(x 2) Also note f(x 1) = f(x 2). a x 2 x 1 The end result is that in the interval (a, b), the graph remains level. Table of Contents b Slide 3

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

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