https://file.aiquickdraw.com/mathbot/file/1726765862886aeerrmw7.jpg

The image shows the graph of a linear function. Let’s determine the domain and range for the linear function based on this graph.

### 1. **Domain**:
The domain of a function represents all the possible values of \(x\) (the horizontal axis) for which the function is defined. Since this is a linear function (a straight line), it extends infinitely in both directions along the x-axis. Therefore, the domain of this function is:
\[
\text{Domain} = (-\infty, \infty)
\]

### 2. **Range**:
The range of a function represents all the possible values of \(y\) (the vertical axis) that the function can output. For a linear function like this one, the line continues indefinitely in both the upward and downward directions along the y-axis. Therefore, the range is also:
\[
\text{Range} = (-\infty, \infty)
\]

So, for this linear function:
- **Domain**: \( (-\infty, \infty) \)
- **Range**: \( (-\infty, \infty) \)

Let me know if you want more detailed explanations or calculations!

Here are five related questions:
1. What is the slope of this line based on the graph?
2. How do you calculate the y-intercept of the line?
3. How do domain and range change for quadratic functions?
4. Can a linear function ever have a limited domain or range?
5. How can you determine the equation of the line from the graph?

**Tip**: For a linear function, the domain and range are always infinite unless the function is restricted to a specific interval.

What are the domain and the range of the linear function based on the given graph?

This page covers the domain and range of a linear function, including a detailed analysis of the graph. Learn how to identify the domain and range for linear functions with an example graph extending infinitely in both directions. Suitable for students in Grades 8-10.

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