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:

Part (b)

Step1: Analyze the graph's trend

The graph of the function (from the given plot) shows that as \( x \) increases (starting from \( x = 0 \) and going to \( +\infty \)), the \( y \)-values are increasing. There is no interval where the function's \( y \)-value decreases as \( x \) increases.

Step2: Determine the correct option

Since the function does not have any interval where it is decreasing (its \( y \)-value never falls as \( x \) increases in the domain shown), we choose option B.

Answer:

B. The function is never decreasing.