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) $(0,\infty)$
(type your answer in interval notation. use a comma to separate answers as needed.)
b. the function is never 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. the function is never decreasing.

Explanation:

Step1: Analyze the function's trend

A function is increasing if, as \(x\) increases, \(y\) also increases. Looking at the graph, from \(x = 0\) to \(x=\infty\), as \(x\) values get larger, \(y\) values are getting larger.

Step2: Check for decreasing and constant

A function is decreasing if as \(x\) increases, \(y\) decreases. There is no part of the graph where this happens. A function is constant if as \(x\) increases, \(y\) remains the same. There is no part of the graph where this happens.

Answer:

(a) A. The function is increasing on the interval(s) \((0,\infty)\)
(b) B. The function is never decreasing
(c) B. The function is never constant