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) . (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's slope

A function is increasing when the slope of the graph is positive (going up - hill as we move from left - to - right).

Step2: Identify increasing intervals

By observing the given graph, we see that the function is increasing on the interval $(-1,4)$.

Step3: Analyze for decreasing intervals

A function is decreasing when the slope of the graph is negative (going down - hill as we move from left - to - right). There are no such intervals in the given graph.

Step4: Analyze for constant intervals

A function is constant when the slope of the graph is zero (horizontal line). There are no such intervals in the given graph.

Answer:

(a) A. The function is increasing on the interval(s) $(-1,4)$
(b) B. The function is never decreasing.
(c) B. The function is never constant.