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
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: Recall function increasing/decreasing rules

A function is increasing if as \(x\) increases, \(y\) increases. It is decreasing if as \(x\) increases, \(y\) decreases.

Step2: Analyze the given graph

Looking at the graph, as \(x\) moves from \(-4\) to \(3\), \(y\) is always getting smaller.

Answer:

a. B. The function is never increasing
b. A. The function is decreasing on the interval \((-4,3)\)