https://file.aiquickdraw.com/mathbot/file/1724682949160xo5d4xjv.jpg

Use the graph to answer the question.

Find the interval(s) over which the function is constant.

To find the interval(s) over which the function is constant, we need to identify where the graph of the function is a horizontal line. A function is constant on an interval if it doesn't increase or decrease, meaning the slope of the graph is zero.

Looking at the graph you provided:

- The function is constant on the interval from \( x = -\infty \) to \( x = -4 \). This is where the graph is a horizontal line, indicating that the function value doesn't change as \( x \) changes.

Thus, the interval over which the function is constant is \( (-\infty, -4] \).

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:

1. How can you determine where a function is increasing or decreasing by looking at its graph?
2. What is the significance of the slope of the graph in determining the behavior of the function?
3. Can a function be constant over multiple intervals, and how would that appear on the graph?
4. How does the derivative of a function relate to the intervals where the function is constant?
5. How would you algebraically determine the intervals over which a function is constant?

**Tip:** When analyzing the graph of a function, always look for flat, horizontal segments to identify intervals where the function is constant.

Learn how to find intervals where a function is constant using graph analysis. This solution explains identifying horizontal segments on the graph as indications of constant function intervals, with a detailed example. Suitable for advanced high school students studying functions and graph analysis.

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