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, ∞).
(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 when, as \(x\) values increase, \(y\) values also increase. Looking at the graph, from \(x =-\infty\) to \(x = 0\), the function is not present (assuming the domain starts at \(x = 0\) or we consider the relevant part). For \(x>0\), as \(x\) increases, \(y\) increases. A function is decreasing when as \(x\) increases, \(y\) decreases. There is no part of the graph where this is happening. A function is constant when as \(x\) increases, \(y\) remains the same. There is no such part in the graph.

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