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State the domain and range for each graph and then tellif the graph is a function (wite yes or no). In set builder notation

The graph you've provided is a horizontal line at \( y = 2 \).

### Domain and Range:

1. **Domain**: The domain of the graph is all the possible values of \( x \). Since the line extends infinitely in both the positive and negative directions along the x-axis, the domain is:
   \[
   \text{Domain} = \{ x \mid x \in \mathbb{R} \}
   \]
   This means that \( x \) can be any real number.

2. **Range**: The range is all the possible values of \( y \). Since the line is horizontal at \( y = 2 \), the range is:
   \[
   \text{Range} = \{ y \mid y = 2 \}
   \]
   This means that \( y \) is always 2.

### Function Status:

- **Is it a function?** Yes, this graph is a function because for every value of \( x \), there is exactly one corresponding value of \( y \) (which is 2 in this case).

**Set Builder Notation**:

- **Domain**: \( \{ x \mid x \in \mathbb{R} \} \)
- **Range**: \( \{ y \mid y = 2 \} \)

Would you like more details on this, or do you have any other questions?

Here are some related questions to expand your understanding:

1. What would the graph look like if the line was at \( y = 5 \)?
2. How would the domain and range change if the line was vertical instead of horizontal?
3. Can you provide an example of a graph that is not a function?
4. What is the significance of a graph passing the vertical line test?
5. How would the domain and range be different for a parabolic graph \( y = x^2 \)?

**Tip:** The vertical line test is a quick way to determine if a graph represents a function—if any vertical line crosses the graph more than once, it's not a function!

Explore how to determine domain, range, and function status of graphs with a focus on set builder notation. Learn about horizontal line graphs and their implications in mathematics. Suitable for students in Grades 9-12.

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