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) (-2, ∞).
(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 function's increasing interval

A function is increasing when, as \(x\) values increase, \(y\) values also increase. Looking at the graph, from \(x = - 2\) to \(+\infty\), as \(x\) gets larger, \(y\) gets larger. So the increasing interval is \((-2,\infty)\).

Step2: Analyze the function's decreasing interval

A function is decreasing when, as \(x\) values increase, \(y\) values decrease. Looking at the graph, from \(-\infty\) to \(x=-2\), as \(x\) gets larger (towards \(-2\)), \(y\) gets smaller. So the decreasing interval is \((-\infty,-2)\)

Answer:

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