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.
a. select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the function is increasing on the interval(s)
(type your answer in interval notation. use a comma to separate answers as needed.)
b. there is no interval on which the function is increasing

Explanation:

Step1: Recall the definition of an increasing function

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

Step2: Analyze the given graph

Looking at the graph, we can see that the function rises (is increasing) for \(x<-1\) and for \(x > 0\). In interval notation, the intervals are \((-\infty,-1)\) and \((0,\infty)\)

Answer:

\((-\infty,-1),(0,\infty)\)