Question

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. there is no interval on which the function is increasing.

Explanation:

Step1: Analyze the graph

Observe the direction of the curve.

Step2: Identify increasing intervals

The function rises from \(x = 1\) to \(+\infty\).

Step3: Write in interval notation

The increasing interval is \((1,\infty)\).

Step4: Identify decreasing intervals

The function falls from \(-\infty\) to \(x = 1\), so the decreasing interval is \((-\infty,1)\).

Step5: Check for constant intervals

The function is never horizontal, so there are no constant - intervals.

Answer:

a. A. The function is increasing on the interval(s) \((1,\infty)\)
b. The function is decreasing on the interval \((-\infty,1)\)
c. There is no open interval on which the function is constant.