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 concept

A function is increasing when the y - values increase as the x - values increase.

Step2: Analyze the graph

Looking at the given graph, as x moves from 1 to positive infinity, the y - values of the function are increasing.

Step3: Write the increasing interval

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

Step4: Recall decreasing - function concept

A function is decreasing when the y - values decrease as the x - values increase.

Step5: Analyze the graph for decreasing part

As x moves from negative infinity to 1, the y - values of the function are decreasing. The decreasing interval is $(-\infty,1)$.

Step6: Recall constant - function concept

A function is constant when the y - values do not change as the x - values change.

Step7: Analyze the graph for constant part

There are no intervals where the function is constant.

Answer:

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