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. the function is decreasing on the interval(s) $(-infty,-1)$
(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: Analyze the function's behavior

A function is increasing when, as \(x\) increases, \(y\) also increases. A function is decreasing when, as \(x\) increases, \(y\) decreases. A function is constant when, as \(x\) increases, \(y\) remains the same.
Looking at the graph:

• For the increasing part:

As \(x\) moves from \(1\) to \(\infty\), the \(y -\) values of the function are increasing. So the interval where the function is increasing is \((1,\infty)\)

• For the decreasing part:

As \(x\) moves from \(-\infty\) to \(1\), the \(y -\) values of the function are decreasing. So the interval where the function is decreasing is \((-\infty,1)\)

• For the constant part:

There is no interval on the graph where, as \(x\) changes, \(y\) remains the same.

Answer:

a. The function is increasing on the interval \((1,\infty)\)
b. The function is decreasing on the interval \((-\infty,1)\)
c. There is no interval on which the function is constant.