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: Analyze the graph's slope

A function is increasing when its slope is positive, decreasing when slope is negative and constant when slope is 0. Looking at the graph, from left - hand side to \(x = - 1\), the function has a slope of 0. From \(x=-1\) to the right, the function has a negative slope.

Step2: Determine increasing intervals

Since the graph does not have any part where the \(y\) - value is getting larger as \(x\) increases, there is no interval where the function is increasing.

Step3: Determine decreasing intervals

The function is decreasing for \(x>-1\). In interval notation, this is \((-1,\infty)\).

Step4: Determine constant intervals

The function is constant for \(x < - 1\). In interval notation, this is \((-\infty,-1)\).

Answer:

a. B. There is no interval on which the function is increasing.
b. The function is decreasing on the interval \((-1,\infty)\)
c. The function is constant on the interval \((-\infty,-1)\)