Question

use the graph to determine
a. open intervals on which the function is decreasing, if any.
b. open intervals on which the function is increasing, 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 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.
b. 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 decreasing intervals

The graph is a line with a positive slope, so it never moves downward as $x$ increases.

Step2: Analyze increasing intervals

The line rises from left to right, so it increases across its entire domain. The $x$-values span from $-5$ to $5$.

Step3: Analyze constant intervals

The line has a consistent positive slope, so it never stays flat.

Answer:

a. B. The function is never decreasing.
b. A. The function is increasing on the interval(s) $(-5, 5)$
c. The function is never constant.