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.

Explanation:

Step1: Analyze the function's trend

A function is increasing if, as \(x\) increases, \(y\) also increases. A function is decreasing if, as \(x\) increases, \(y\) decreases. A function is constant if, as \(x\) increases, \(y\) remains the same.
Looking at the given graph, we observe that for all values of \(x\) (from \(-\infty\) to \(\infty\)), as \(x\) increases, \(y\) is also increasing.

Step2: Determine intervals

Since the function is always increasing and never decreasing or constant.

Answer:

(a) \((-\infty,\infty)\)
(b) There are no such intervals.
(c) There are no such intervals.