https://r2.erweima.ai/mathbot/image/1724981785366ddcfqu70.jpg

The image shows a graph of a function that appears to be a piecewise linear function with three segments. 

### Analyzing the Graph:

- The function has two horizontal line segments from \( x = -6 \) to \( x = 6 \), both at \( y = 6 \).
- From \( x = -6 \) to \( x = -\infty \), the graph decreases downwards.
- Similarly, from \( x = 6 \) to \( x = \infty \), the graph also decreases downwards.

### Range of the Function:
The range is the set of all possible \( y \)-values that the function can take.

1. The function has values at \( y = 6 \) between \( x = -6 \) and \( x = 6 \).
2. The function decreases towards \( y = -\infty \) as \( x \) moves away from \( -6 \) and \( 6 \) towards negative and positive infinity, respectively.

Thus, the range in interval notation is:
\[
(-\infty, 6]
\]

This represents all values from \( y = -\infty \) up to and including \( y = 6 \).

Would you like more details or have any further questions? Here are some related questions:

1. What is the domain of this function?
2. How do you determine if a function is increasing or decreasing?
3. What is the importance of interval notation in describing the range?
4. How would the graph change if the horizontal segment were at \( y = 8 \) instead of \( y = 6 \)?
5. Can a function have a range that includes all real numbers?

**Tip:** When dealing with graphs, always pay attention to where the function increases or decreases, as this helps in determining the range.

Explore how to determine the range of piecewise linear functions in interval notation. This problem involves analyzing a graph with multiple segments and identifying the range of function values. Suitable for students in Grades 9-12.

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