Question

identify the increasing and decreasing; decreasing: (-∞,0),(2,∞) increasing: (-∞,0),(2,∞) increasing: (0,1),(1,2) decreasing: (0,1),(1,2) clear all

Explanation:

Step1: Recall increasing - decreasing rules

A function is increasing when the slope is positive and decreasing when the slope is negative.

Step2: Analyze the graph

By observing the graph, in the intervals $(-\infty,0)$ and $(2,\infty)$ the function is going down - slope is negative, so it is decreasing. In the intervals $(0,1)$ and $(1,2)$ the function is going up - slope is positive, so it is increasing.

Answer:

Decreasing: $(-\infty,0),(2,\infty)$; Increasing: $(0,1),(1,2)$