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
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
a. 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

Explanation:

Step1: Analyze the function's trend

A function is increasing when, as \(x\) values increase, \(y\) values also increase. A function is decreasing when, as \(x\) values increase, \(y\) values decrease. A function is constant when \(y\) values remain the same as \(x\) values change.
Looking at the graph, we check for intervals where \(y\) decreases as \(x\) increases.

Step2: Determine the decreasing interval

From the graph, we observe that as \(x\) moves from \(-\infty\) to \(2\), the \(y -\) values are decreasing.

Answer:

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