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
c. select the correct choice below and, if necessary, fill in the answer box to complete your choice
a. the function is constant on the interval(s)
(type your answer in interval notation. use a comma to separate answers as needed.)

Explanation:

Step1: Determine increasing interval

A function is increasing when, as \(x\) increases, \(y\) also increases. Looking at the graph, we can see that the function is increasing on the interval \((-\infty, 2)\).

Step2: Determine decreasing interval

A function is decreasing when, as \(x\) increases, \(y\) decreases. From the graph, the function is decreasing on the interval \((2,4)\).

Step3: Determine constant interval

A function is constant when, as \(x\) changes, \(y\) remains the same. There is no such interval in this graph.

Answer:

a. A. The function is increasing on the interval(s) \((-\infty, 2)\)
b. A. The function is decreasing on the interval(s) \((2,4)\)
c. B. There is no interval on which the function is constant.