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. the function is never increasing

Explanation:

Step1: Identify increasing interval

A function increases when its graph rises from left to right. From the graph, this starts at $x=2$ and continues infinitely right.
Interval: $(2, \infty)$

Step2: Identify decreasing interval

A function decreases when its graph falls from left to right. The graph never falls as $x$ increases, so there is no decreasing interval.

Step3: Identify constant interval

A function is constant when its graph is horizontal. From the graph, this occurs for $x$ from $-\infty$ to $2$.
Interval: $(-\infty, 2)$

Answer:

(a) A. The function is increasing on the interval(s) $(2, \infty)$
(b) B. The function is never decreasing
(c) The function is constant on the interval $(-\infty, 2)$