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. 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.

(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.)
○ b. the function is never constant.

Explanation:

Step1: Analyze increasing interval

A function is increasing if, as \(x\) increases, \(y\) also increases. Looking at the graph, from \(-\infty\) to \(\infty\), as \(x\) increases, \(y\) is always increasing.

Step2: Analyze decreasing interval

A function is decreasing if, as \(x\) increases, \(y\) decreases. Since the function is always increasing, it is never decreasing.

Step3: Analyze constant interval

A function is constant if, as \(x\) increases, \(y\) remains the same. Since the function is always increasing, it is never constant.

Answer:

(a) A. The function is increasing on the interval\((-\infty,\infty)\)
(b) B. The function is never decreasing.
(c) B. The function is never constant.