the function f is graphed below. determine the intervals on which f is increasing and decreasing. answer…

Explanation:

Step1: Recall increasing - decreasing rules

A function is increasing when the graph goes up from left - to - right and decreasing when it goes down from left - to - right.

Step2: Analyze segment 1

Looking at the left - most part of the graph, it is going up from (x=-4) to (x = - 1). So, the function is increasing on the interval (-4<x<-1).

Step3: Analyze segment 2

The middle part of the graph is going down from (x=-1) to (x = 1). So, the function is decreasing on the interval (-1<x<1).

Step4: Analyze segment 3

The right - most part of the graph is going down from (x = 1) to (x=4). So, the function is decreasing on the interval (1<x<4).

Answer:

The function is increasing on the interval (-4<x<-1), decreasing on the interval (-1<x<1), and decreasing on the interval (1<x<4).