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.
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. there is no interval on which the function is decreasing

Explanation:

Step1: Analyze the increasing intervals

A function is increasing when, as \(x\) increases, \(y\) also increases. Looking at the graph, there is no such part where \(y\) increases as \(x\) increases.

Step2: Analyze the decreasing intervals

A function is decreasing when, as \(x\) increases, \(y\) decreases. From \(x = 0\) to \(+\infty\), as \(x\) increases, \(y\) decreases. But wait, for \(x\in(-\infty,0)\), the function is constant (horizontal line). So the function is decreasing on \((0,\infty)\)

Step3: Analyze the constant intervals

A function is constant when \(y\) does not change as \(x\) changes. For \(x\in(-\infty,0)\), \(y = - 4\) (horizontal line), so the function is constant on \((-\infty,0)\)

Answer:

a. B. There is no interval on which the function is increasing
b. A. The function is decreasing on the interval(s) \((0,\infty)\)
c. A. The function is constant on the interval(s) \((-\infty,0)\)