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