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

Explanation:

Step1: Understand increasing intervals

A function is increasing when as $x$ increases, $y$ also increases. Looking at the graph, we see the function rises from $x = 1$ to the right.

Step2: Write the interval

In interval - notation, the open interval on which the function is increasing is $(1,\infty)$.

Step3: Analyze decreasing intervals

A function is decreasing when as $x$ increases, $y$ decreases. The function falls from negative - infinity to $x = 1$, so the decreasing interval is $(-\infty,1)$.

Step4: Analyze constant intervals

A function is constant when $y$ does not change as $x$ changes. There are no such intervals in this graph.

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.