https://file.aiquickdraw.com/mathbot/file/1723679060259hbid8smn.jpg

The graph you've provided shows a piecewise linear function. To find the domain and range of this function, we'll analyze the graph:

### Domain:
The domain of a function is the set of all possible input values (x-values) for which the function is defined.

- From the graph, the function starts at \(x = 0\) and ends at \(x = 6\). The function is defined for all x-values within this interval.
- Therefore, the domain is \( [0, 6] \).

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

- The minimum y-value on the graph occurs at \(y = 4\), and the maximum y-value occurs at \(y = 12\).
- Therefore, the range is \( [4, 12] \).

### Summary:
- **Domain:** \( [0, 6] \)
- **Range:** \( [4, 12] \)

Would you like further details or explanations? 

Here are some additional related questions you might find useful:

1. How do you find the domain and range for other types of functions?
2. What does it mean if a function's domain or range is infinite?
3. How can you determine the domain and range from an equation instead of a graph?
4. What are piecewise functions, and how are they different from regular functions?
5. How do vertical and horizontal line tests relate to the domain and range?
6. Can the domain and range of a function include negative numbers?
7. How would the domain and range change if the graph were shifted vertically or horizontally?
8. How do the concepts of increasing and decreasing intervals relate to the range of a function?

**Tip:** When determining the domain and range from a graph, always check the start and end points of the graph, and identify any gaps or restrictions in the x- and y-values.

Learn how to find the domain and range of a piecewise linear function using a graph analysis approach. Understand the concepts of domain (input values) and range (output values) with detailed examples. Suitable for students in Grades 9-12.

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