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. the function is never increasing.

Explanation:

Step1: Analyze the graph

A function is increasing when, as \(x\) values increase, \(y\) values also increase. Looking at the given graph, we observe that for \(x > - 2\), as \(x\) moves to the right (increases), \(y\) also moves upwards (increases).

Step2: Write the interval in interval notation

The interval where the function is increasing is \((-2,\infty)\)

Answer:

A. The function is increasing on the interval(s) \((-2,\infty)\)