https://file.aiquickdraw.com/mathbot/file/1726765688822gkogn0zj.jpg

what are the domain and range of this linear function?

The graph in the image shows a **horizontal line** at \( y = 2 \). This indicates that the function is a constant linear function, meaning that for all values of \( x \), the output (or \( y \)-value) is always \( 2 \).

### Domain:
The domain of a function is the set of all possible input values (in this case, \( x \)-values). Since this is a linear function that extends infinitely in both directions along the \( x \)-axis, the domain includes all real numbers.

- **Domain:** \( (-\infty, \infty) \) or "all real numbers."

### Range:
The range of a function is the set of all possible output values (in this case, \( y \)-values). For this graph, the \( y \)-value is always \( 2 \) no matter the \( x \)-value, so the range consists of just the single value \( 2 \).

- **Range:** \( \{ 2 \} \).

Would you like more details on how the domain and range are determined?

Here are 5 related questions you might find useful:
1. What is the general form of a constant function?
2. How do you find the slope of a horizontal line?
3. Can a linear function ever have a limited domain or range?
4. What is the difference between a horizontal and vertical line on a graph?
5. How would the domain and range change if the graph were a vertical line instead?

**Tip:** In a linear equation \( y = mx + b \), if \( m = 0 \), the function is constant, and the graph is a horizontal line.

What are the domain and range of this linear function?

Explore the domain and range of a linear function shown as a horizontal line at y = 2. Understand how the domain includes all real numbers while the range consists of a single constant value. Suitable for students in Grades 6-8 learning linear functions.

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