Question

use the graph to determine (a) open intervals on which the function is increasing, if any. (b) open intervals on which the function is decreasing, if any. (c) open intervals on which the function is constant, if any.

Explanation:

Step1: Recall increasing - function definition

A function $y = f(x)$ is increasing on an open interval if for any two points $x_1$ and $x_2$ in the interval with $x_1

Step2: Recall decreasing - function definition

A function $y = f(x)$ is decreasing on an open interval if for any two points $x_1$ and $x_2$ in the interval with $x_1f(x_2)$. The function is decreasing on the intervals $(-1,1)$ and $(5,6)$.

Step3: Recall constant - function definition

A function $y = f(x)$ is constant on an open interval if for any two points $x_1$ and $x_2$ in the interval, $f(x_1)=f(x_2)$. There are no such intervals where the function is constant.

Answer:

(a) $(1,2),(4,5)$
(b) $(-1,1),(5,6)$
(c) None