use the graph to determine\na. open intervals on which the function is increasing, if any.\nb. open…

Explanation:

Step1: Recall increasing - function definition

A function is increasing on an open interval if, for any two points $x_1$ and $x_2$ in the interval with $x_1<x_2$, then $f(x_1)<f(x_2)$. Looking at the graph, we see that the function is rising from $x = - 1$ to the right.

Step2: Determine increasing interval

The function is increasing on the open interval $(-1,\infty)$.

Step3: Recall decreasing - function definition

A function is decreasing on an open interval if, for any two points $x_1$ and $x_2$ in the interval with $x_1<x_2$, then $f(x_1)>f(x_2)$. The function is falling from negative infinity to $x=-1$.

Step4: Determine decreasing interval

The function is decreasing on the open interval $(-\infty,-1)$.

Step5: Recall constant - function definition

A function 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 on this graph.

Answer:

a. $(-1,\infty)$ b. $(-\infty,-1)$ c. None