Question

consider the graph of a function ( f ) shown below.

use the graph to estimate the sets on which ( f ) is increasing and decreasing.

use intervals connected by ( cup ) as needed. e.g., ( (-infty, -5) ) or ( (0, 2) cup (6, 7) ).

a). increasing:

b). decreasing:

Explanation:

Step1: Identify increasing intervals

A function is increasing when its graph rises from left to right. From the graph, this occurs on $(-\infty, -2)$ and $(6, \infty)$.

Step2: Identify decreasing intervals

A function is decreasing when its graph falls from left to right. From the graph, this occurs on $(-2, 2)$ and $(2, 6)$.

Answer:

a). Increasing: $(-\infty, -2) \cup (6, \infty)$
b). Decreasing: $(-2, 2) \cup (2, 6)$