https://file.aiquickdraw.com/mathbot/file/1726273230754rinrw0uj.jpg

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.

Let's analyze the graph to answer the three parts of the question.

### (a) **Open intervals where the function is increasing:**

A function is increasing on an interval when the graph moves upwards as you move from left to right.

- The function increases between \(x = -5\) and \(x = -3\), and again between \(x = -2\) and \(x = 0\).

Thus, the open intervals where the function is increasing are:
\[
(-5, -3) \cup (-2, 0)
\]

### (b) **Open intervals where the function is decreasing:**

A function is decreasing on an interval when the graph moves downwards as you move from left to right.

- The function decreases from \(x = -7\) to \(x = -5\), from \(x = -3\) to \(x = -2\), and from \(x = 0\) to \(x = 2\).

Thus, the open intervals where the function is decreasing are:
\[
(-7, -5) \cup (-3, -2) \cup (0, 2)
\]

### (c) **Open intervals where the function is constant:**

A function is constant on an interval when the graph is flat (horizontal).

- In this case, the graph has no flat or horizontal parts, so the function is not constant anywhere.

Thus, there are no intervals where the function is constant:
\[
\text{None}
\]

Would you like more details on any part of this? Here are five related questions that might interest you:

1. How do you identify turning points on a graph?
2. What is the difference between increasing and strictly increasing functions?
3. Can a function be both increasing and decreasing on the same interval?
4. How do you determine local maxima and minima from a graph?
5. How would the behavior of this function change if we shifted it vertically?

**Tip:** Always observe the graph carefully to detect whether the function has flat sections for constant intervals, even if they are small.

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.

Determine the open intervals where the function is increasing, decreasing, or constant by analyzing a graph. This graph analysis is suitable for high school students in Grades 9-12 and covers key concepts of function behavior on intervals.

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