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) $(1,\infty)$
(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.
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.)
b. there is no interval on which the function is decreasing.

Explanation:

Step1: Analyze the graph for increasing intervals

A function is increasing when, as \(x\) increases, \(y\) also increases. Looking at the graph, from \(x = 1\) to \(x=\infty\), as \(x\) values get larger, \(y\) values get larger. So the increasing interval is \((1,\infty)\).

Step2: Analyze the graph for decreasing intervals

A function is decreasing when, as \(x\) increases, \(y\) decreases. Looking at the graph, from \(x=-\infty\) to \(x = 1\), as \(x\) values get larger, \(y\) values get smaller. So the decreasing interval is \((-\infty,1)\).

Step3: Analyze the graph for constant intervals

A function is constant when, as \(x\) increases, \(y\) remains the same. Looking at the graph, there is no part where \(y\) is constant as \(x\) changes.

Answer:

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