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 increasing - function definition

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

Step2: Observe the graph

Looking at the graph, we see that as \(x\) moves from \(- 3\) to \(0\), the \(y\) - values of the function are getting larger.

Step3: Write the increasing interval

The function is increasing on the interval \((-3,0)\).

Step4: Recall decreasing - function definition

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

Step5: Observe the graph for decreasing part

As \(x\) moves from \(0\) to \(3\), the \(y\) - values of the function are getting smaller. So the function is decreasing on the interval \((0,3)\).

Step6: Recall constant - function definition

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

Step7: Observe the graph for constant part

There are no horizontal segments on the graph, so the function is not constant on any open interval.

Answer:

a. A. The function is increasing on the interval(s) \((-3,0)\)
b. The function is decreasing on the interval \((0,3)\)
c. There is no open interval on which the function is constant.