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 interval

Observe the graph: as $x$ increases, $y$ rises across all visible $x$-values, from $-\infty$ to $+\infty$.

Step2: Analyze decreasing interval

Check for $x$ where $y$ falls as $x$ rises: no such interval exists.

Step3: Analyze constant interval

Check for $x$ where $y$ stays flat: no such interval exists.

Answer:

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