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.
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 decreasing intervals

A function decreases when y falls as x rises. For the given line, y decreases as x increases. The x-values span from $-\infty$ to $+\infty$.
Interval: $(-\infty, \infty)$

Step2: Analyze increasing intervals

A function increases when y rises as x rises. The line has a negative slope, so y never rises with x.

Step3: Analyze constant intervals

A function is constant when y does not change with x. The line has a non-zero slope, so y always changes with x.

Answer:

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