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: Identify increasing interval

A function increases when its graph rises from left to right. Looking at the parabola, it rises from $x=-\infty$ to $x=2$.

Step2: Identify decreasing interval

A function decreases when its graph falls from left to right. The parabola falls from $x=2$ to $x=+\infty$.

Step3: Check for constant interval

A constant function has a horizontal graph; this graph has no horizontal segments.

Answer:

a. A. The function is increasing on the interval(s) $(-\infty, 2)$
b. The function is decreasing on the interval(s) $(2, \infty)$
c. B. There is no interval on which the function is constant.