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. the function is never increasing.

Explanation:

Step1: Recall increasing - function definition

A function is increasing when as \(x\) increases, \(y\) increases.

Step2: Analyze the graph

Looking at the graph, we see that as \(x\) moves from - 1 to 1, \(y\) values are going up.
The interval is \((-1,1)\).

Step3: Recall decreasing - function definition

A function is decreasing when as \(x\) increases, \(y\) decreases.

Step4: Analyze the graph for decreasing part

As \(x\) moves from - 7 to - 1 and from 1 to 7, \(y\) values are going down. The intervals are \((-7,-1)\) and \((1,7)\).

Step5: Recall constant - function definition

A function is constant when \(y\) values do not change as \(x\) changes.

Step6: Analyze the graph for constant part

There are no intervals where \(y\) is constant.

Answer:

(a) A. The function is increasing on the interval(s) \((-1,1)\)
(b) The function is decreasing on the intervals \((-7,-1),(1,7)\)
(c) The function is never constant.