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: Analyze the function's trend

A function is increasing if, as \(x\) increases, \(y\) also increases. A function is decreasing if, as \(x\) increases, \(y\) decreases. A function is constant if, as \(x\) increases, \(y\) remains the same.
Looking at the graph, as \(x\) increases from \(-5\) to \(6\), \(y\) is decreasing. There is no interval where \(y\) is increasing (since the slope is negative throughout the domain shown). Also, there is no interval where the function is constant (no horizontal line segment in the graph).

Step2: Determine the decreasing interval

The domain of the function (based on the graph's endpoints) is from \(x=-5\) to \(x = 6\). Since the function is decreasing over its entire domain (as \(x\) moves from \(-5\) to \(6\), \(y\) is going down), the interval of decrease is \((-5,6)\)

Answer:

a. B. The function is never increasing.
b. A. The function is decreasing on the interval(s) \((-5,6)\)
c. B. The function is never constant.