Decreasing Function

A function is decreasing when its output decreases as the input increases, meaning that as one moves from left to right along the x-axis, the f(x)-values on the graph get smaller.

This behavior is identified by observing whether the graph slopes downward from left to right.

Consider a man running on a track. The time taken and the distance covered for each lap are recorded to determine changes in speed over different intervals.

The average speed—or rate of change—between intervals is determined by calculating the change in distance and dividing it by the change in time between two recorded points.

Next, to identify whether the speed is increasing or decreasing, each lap’s speed is calculated by dividing the distance covered by the time taken for that lap. This helps analyze how the runner’s pace changes from one lap to the next.

When plotted as a speed-versus-time graph, the data shows a consistent decline in speed. This represents a decreasing function, confirming that the runner slows down with each successive lap.

The concept of decreasing functions models various situations where outputs decrease with increasing input, such as battery life or cooling temperature.