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

The image depicts a triangle plotted on a coordinate plane. To analyze the domain, range, and whether the graph represents a function, let's consider the following:

### Domain and Range:

1. **Domain:** The domain is the set of all possible x-values that the graph covers.
   - From the graph, the x-values range from approximately \( x = -5 \) to \( x = 3 \).
   - In set-builder notation, the domain is:
     \[
     \{ x \mid -5 \leq x \leq 3 \}
     \]

2. **Range:** The range is the set of all possible y-values that the graph covers.
   - From the graph, the y-values range from approximately \( y = -4 \) to \( y = 5 \).
   - In set-builder notation, the range is:
     \[
     \{ y \mid -4 \leq y \leq 5 \}
     \]

### Is it a function?

- A graph represents a function if every x-value (input) corresponds to exactly one y-value (output).
- The given graph fails the **vertical line test** because there are vertical lines that intersect the graph at more than one point (for instance, around \( x = -2 \) and \( x = 1 \)).
- Therefore, **the graph is not a function.** (Answer: **No**)

Would you like more details or have any questions?

Here are five related questions you might consider:
1. What is the vertical line test, and how does it determine if a graph is a function?
2. How do you find the range and domain of a more complex function?
3. What are some common shapes of graphs that do not represent functions?
4. Can a graph represent a function if the domain or range is restricted to a smaller set?
5. How can transformations (like translations or reflections) affect the domain and range of a graph?

**Tip:** When determining if a graph is a function, always check if any vertical line intersects the graph at more than one point. This simple test can save time and ensure accuracy.

Understand how to analyze the domain, range, and whether a graph represents a function using set builder notation. Explore the vertical line test and its role in determining function status. Suitable for high school students.

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