https://file.aiquickdraw.com/mathbot/file/1729451536009dora1lzv.jpg

Answer for the following questions about the graph below. Answer in interval notation. Answer DNE if the interval does not exist.

a. In what interval(s) is the function is increasing?
b. In what interval(s) is the function is decreasing?
c. In what interval(s) is the function is constant?

Let's analyze the graph step by step to answer the questions in interval notation.

### a. In what interval(s) is the function increasing?

The function increases where the slope of the graph is positive. By inspecting the graph:
- From \(x = -3\) to \(x = -1\), the graph increases as it rises from \(y = -2\) to \(y = 0\).
- From \(x = 1\) to \(x = 3\), the graph increases as it rises from \(y = 0\) to \(y = 3\).

So, the function is increasing on the intervals:
\[
\boxed{(-3, -1) \cup (1, 3)}
\]

### b. In what interval(s) is the function decreasing?

The function decreases where the slope of the graph is negative. From the graph:
- From \(x = -1\) to \(x = 0\), the graph decreases from \(y = 0\) to \(y = 2\).
- From \(x = 0\) to \(x = 1\), the graph decreases from \(y = 2\) to \(y = 0\).

So, the function is decreasing on the interval:
\[
\boxed{(-1, 0) \cup (0, 1)}
\]

### c. In what interval(s) is the function constant?

The function is constant where the graph is flat (i.e., horizontal), and there are no such intervals in this graph. Therefore:
\[
\boxed{\text{DNE}}
\]

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Let me know if you'd like further clarification or details!

Here are five related questions for further practice:
1. What are the local maxima and minima of the function?
2. How would you describe the symmetry of this function, if any?
3. What are the intercepts of the function?
4. Over what intervals is the function positive?
5. Over what intervals is the function negative?

**Tip:** When analyzing functions graphically, always observe the slope of the graph to determine increasing or decreasing behavior.

Answer for the following questions about the graph below. Answer in interval notation. Answer DNE if the interval does not exist.

a. In what interval(s) is the function increasing?
b. In what interval(s) is the function decreasing?
c. In what interval(s) is the function constant?

Learn how to analyze the intervals where a function is increasing, decreasing, or constant by interpreting its graph. The problem includes step-by-step solutions with clear interval notation, ideal for students in Grades 9-12 studying algebra and graphing functions.

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