decreasing function
[decreasing function|decreasing function] refers to a function where the slope is negative.
Definition
decreasing function refers to a function where the slope is negative. It is defined on an open interval, such that for any two input values a and b in the interval, if b > a then f(b) < f(a). The function's decreasing nature is determined by the relationship between input values and their corresponding output values within the specified interval.
Mechanism
decreasing function The average rate of change for a decreasing function is negative, contrasting with increasing functions which have a positive average rate of change. [link] illustrates examples of increasing and decreasing intervals on a function. A function f is considered decreasing on an open interval if f(b) < f(a) for any two inputs a and b where b > a.
Causes
decreasing function The decreasing function is identified by the condition A < 0. This mathematical property indicates a negative slope in the function's graph. The note specifies that this characteristic defines the function's behavior.
Effects
decreasing function [decreasing function] indicates a relationship where the output decreases as the input increases. This behavior is confirmed by the condition A < 0, which establishes the function's decreasing nature. The note explicitly identifies this characteristic, reinforcing the functional relationship.
Examples
decreasing function has a negative average rate of change. The average rate of change for decreasing function is negative, contrasting with increasing functions. [link] provides examples of decreasing intervals on a function.
Average Rate Mechanism
decreasing function exhibits a negative average rate of change. This mechanism calculates the average rate by dividing the total change in output by the total change in input, reflecting the function's decreasing nature as input increases.
Open Interval
decreasing function [decreasing function] is defined on an open interval when for any two input values a and b within the interval, where b > a, the function satisfies f(b) < f(a). This condition applies specifically to the open interval, distinguishing it from other interval types. The relationship between input values and their corresponding function values determines the function's decreasing nature over the interval.