15. f is increasing on the open intervals , , and . f is decreasing on the open intervals , , , and .

Explanation:

Step1: Recall increasing - decreasing function concept

A function $y = f(x)$ is increasing on an open interval if for any two points $x_1,x_2$ in the interval with $x_1<x_2$, $f(x_1)<f(x_2)$, and decreasing if $f(x_1)>f(x_2)$. Visually, an increasing function has a positive - slope and a decreasing function has a negative - slope.

Step2: Identify increasing intervals from the graph

By observing the graph, we see that the function is increasing when the curve is going up from left to right. The function $f(x)$ is increasing on the intervals $(-9,-6)$, $(1,3)$ and $(7,8)$.

Step3: Identify decreasing intervals from the graph

By observing the graph, we see that the function is decreasing when the curve is going down from left to right. The function $f(x)$ is decreasing on the intervals $(-11,-9)$, $(-6,1)$, $(3,7)$ and $(8,10)$.

Answer:

$f$ is increasing on the open intervals $(-9,-6)$, $(1,3)$, and $(7,8)$. $f$ is decreasing on the open intervals $(-11,-9)$, $(-6,1)$, $(3,7)$, and $(8,10)$.