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.
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
-6
-4
-2
2
4
x
y



A coordinate system has a horizontal x-axis labeled from negative 7 to 7 in increments of 1 and a vertical y-axis labeled from negative 6 to 4 in increments of 1. From left to right, a curve rises at a decreasing rate and comes to a maximum at (2, 0). The curve then falls, first at an increasing rate, and then at a decreasing rate until it reaches a minimum at (3, negative 1). The curve then rises, first at an increasing rate, and then at a decreasing rate until it reaches a maximum at (4, 0). The curve then falls at an increasing rate for the rest of the graph..
Question content area bottom
Part 1
​(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)
  
enter your response here.
​(Type your answer in interval notation. Use a comma to separate answers as​ needed.)
B.
The function is never increasing.
Part 2
​(b) 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)
  
enter your response here.
​(Type your answer in interval notation. Use a comma to separate answers as​ needed.)
B.
The function is never decreasing.
Part 3
​(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)
  
enter your response here.
​(Type your answer in interval notation. Use a comma to separate answers as​ needed.)
B.
The function is never constant.

Answer 1

Based on your description of the graph, we can analyze the behavior of the function based on the intervals where it is increasing, decreasing, or constant.

**Part 1: (a) Increasing Intervals**
The function is rising until it reaches the maximum at (2, 0) and then after (3, -1), it rises again until it reaches (4, 0). The function is increasing on the following intervals:

- From \( x = -7 \) to \( x = 2 \) (specifically \( (-7, 2) \))
- From \( x = 3 \) to \( x = 4 \) (specifically \( (3, 4) \))

Thus, the increasing intervals are:
\[
\text{The function is increasing on the intervals } (-7, 2) \text{ and } (3, 4).
\]

**Part 2: (b) Decreasing Intervals**
The function decreases between the maximum at (2, 0) and the minimum at (3, -1). The only decreasing interval is:

- From \( x = 2 \) to \( x = 3 \) (specifically \( (2, 3) \))

Thus, the decreasing interval is:
\[
\text{The function is decreasing on the interval } (2, 3).
\]

**Part 3: (c) Constant Intervals**
From your description, the function does not remain constant at any interval. It continuously changes either by increasing or decreasing.

Thus, we can conclude:
\[
\text{The function is never constant.}
\]

In summary:
- **(a)** Increasing: \( (-7, 2) \) and \( (3, 4) \)
- **(b)** Decreasing: \( (2, 3) \)
- **(c)** Constant: Never constant.