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.

oa. the function is increasing on the interval(s)
(type your answer in interval notation. use a comma to separate answers as needed.)
ob. there is no interval on which the function is increasing.

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

c. select the correct choice below and, if necessary, fill in the answer box to complete your choice.
oa. the function is constant on the interval(s)
(type your answer in interval notation. use a comma to separate answers as needed.)

Explanation:

Step1: Analyze the function's increasing intervals

A function is increasing when, as \(x\) increases, \(y\) also increases. Looking at the graph, there is no such interval where this occurs.

Step2: Analyze the function's decreasing intervals

A function is decreasing when, as \(x\) increases, \(y\) decreases. From the graph, we can see that as \(x\) moves from \(2\) to \(6\), \(y\) decreases. In interval notation, this is \((2,6)\).

Step3: Analyze the function's constant intervals

A function is constant when, as \(x\) increases, \(y\) remains the same. Looking at the graph, there is no such interval where this occurs.

Answer:

a. B. There is no interval on which the function is increasing.
b. A. The function is decreasing on the interval(s) \((2,6)\)
c. B. There is no interval on which the function is constant.