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.

Explanation:

Step1: Analyze increasing intervals

A function is increasing on an open interval if as $x$ increases, $y$ increases. Looking at the graph, as $x$ moves from $-\infty$ to $+\infty$, the $y$-values consistently rise.

Step2: Analyze decreasing intervals

A function is decreasing if as $x$ increases, $y$ decreases. The graph shows no such interval where $y$ falls as $x$ rises.

Step3: Analyze constant intervals

A function is constant if $y$ does not change as $x$ increases. The graph has no flat segments, so no constant intervals.

Answer:

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