https://file.aiquickdraw.com/mathbot/file/1726076474715pbmrhh12.jpg

This graph shows a linear function that extends from \((-10, -8)\) to approximately \((10, 7)\) on the coordinate plane. The question asks for the **domain** of this function.

Since the graph represents a linear function and the line extends indefinitely in both the left and right directions, the domain includes all possible \(x\)-values. In mathematical terms, the domain of a linear function is **all real numbers**, as there is no restriction on \(x\).

Thus, the domain can be written as:

\[
\boxed{x \in (-\infty, \infty)}
\]
or
\[
\boxed{(-\infty, \infty)}
\]

Would you like further clarification or have additional questions?

Here are some related questions to expand on the topic:
1. How do we determine the range of a linear function?
2. What is the slope of this linear function, and how can we calculate it from the graph?
3. Can the domain of a function ever be restricted? If so, how?
4. How does the domain differ between linear and other types of functions, such as quadratics or rational functions?
5. How would the domain change if the graph were part of a piecewise function?

**Tip:** The domain of most functions can be found by identifying which \(x\)-values are possible inputs, and checking for restrictions such as divisions by zero or square roots of negative numbers.

What is the domain of the function shown in the graph of a linear function?

Learn how to find the domain of a linear function from a graph. This problem demonstrates how the domain for linear functions is typically all real numbers. Suitable for students in Grades 7-9.

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