https://file.aiquickdraw.com/mathbot/file/1724557385983wxt67vrv.jpg

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

Let's analyze the two graphs shown in the image:

### Left Graph:
- **Domain**: The domain is the set of all possible x-values. The graph is a vertical line at \( x = -3 \). Therefore, the domain is:
  \[
  \{ x \, | \, x = -3 \}
  \]

- **Range**: The range is the set of all possible y-values. Since the vertical line extends infinitely in both directions along the y-axis, the range is all real numbers:
  \[
  \{ y \, | \, y \in \mathbb{R} \}
  \]

- **Is it a function?**: No, this graph is not a function. A vertical line test would show that multiple y-values correspond to the single x-value of \(-3\), which violates the definition of a function.

### Right Graph:
- **Domain**: The domain is the set of all possible x-values. The graph is a single point at \( x = 2 \). Therefore, the domain is:
  \[
  \{ x \, | \, x = 2 \}
  \]

- **Range**: The range is the set of all possible y-values. The graph is a single point at \( y = 3 \). Therefore, the range is:
  \[
  \{ y \, | \, y = 3 \}
  \]

- **Is it a function?**: Yes, this graph is a function. Each x-value corresponds to exactly one y-value.

Would you like any further details or explanations?

### Related Questions:
1. What is the vertical line test, and how does it determine if a graph is a function?
2. Can a single point on a graph ever not be a function?
3. How does the domain differ when dealing with parabolas or quadratic functions?
4. What happens to the domain and range when the graph of a function is shifted horizontally or vertically?
5. What is the difference between a continuous and a discrete domain?

### Tip:
When determining if a graph is a function, always remember that for each x-value, there should be only one corresponding y-value.

Explore how to determine if a graph represents a function by analyzing its domain, range, and applying the vertical line test. Includes examples and explanations for various graph types.

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