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. there is no interval on which the function is increasing

Explanation:

Step1: Recall the definition of increasing, decreasing and constant functions

A function \(y = f(x)\) is increasing on an interval if for any \(x_1

Step2: Analyze the graph for increasing intervals

Looking at the graph, as \(x\) - values increase, the \(y\) - values do not increase. So, there is no interval where the function is increasing.

Step3: Analyze the graph for decreasing intervals

For \(x\in(-\infty,3)\), as \(x\) increases (moving from left to right on the \(x\) - axis), the \(y\) - values decrease. In interval notation, the function is decreasing on \((-\infty,3)\)

Step4: Analyze the graph for constant intervals

For \(x\in(3,\infty)\), as \(x\) increases, the \(y\) - values remain the same (equal to \(1\)). In interval notation, the function is constant on \((3,\infty)\)

Answer:

a. B. There is no interval on which the function is increasing.
b. The function is decreasing on the interval \((-\infty,3)\)
c. The function is constant on the interval \((3,\infty)\)