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.
(type your answer in interval notation. use a comma to separate answers as needed.)
a. 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 function increasing

A function is increasing if as \(x\) increases, \(y\) increases. Looking at the graph, there is no such interval. So for part a, the function is never increasing.

Step2: Analyze function decreasing

A function is decreasing if as \(x\) increases, \(y\) decreases. The graph is a straight - line (linear function) with a negative slope. The domain of the function (assuming it is defined for all \(x\) between the two endpoints of the line segment) is from \(x=-4\) to \(x = 2\). In interval notation, the function is decreasing on the interval \((-4,2)\)

Answer:

a. B. The function is never increasing.
b. A. The function is decreasing on the interval \((-4,2)\)