Question

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

Explanation:

Step1: Recall increasing - decreasing definition

A function $y = f(x)$ is increasing when as $x$ increases, $y$ increases and decreasing when as $x$ increases, $y$ decreases.

Step2: Analyze the graph segments

Looking at the graph, from $x=-9$ to $x = - 4$, as $x$ increases, $y$ decreases. From $x=-4$ to $x = 2$, as $x$ increases, $y$ increases. From $x = 2$ to $x=7$, as $x$ increases, $y$ decreases.

Answer:

The function $f$ is increasing on the interval $(-4,2)$ and decreasing on the intervals $(-9,-4)$ and $(2,7)$.