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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

To analyze the graph:

### 1. **Domain:**
   The domain of a graph is the set of all possible \( x \)-values (inputs) for which the graph has points.

   **Domain in Set-Builder Notation:**
   \[
   \{ x \mid -4 \leq x \leq 6 \}
   \]
   The graph extends horizontally from \( x = -4 \) to \( x = 6 \).

### 2. **Range:**
   The range of a graph is the set of all possible \( y \)-values (outputs) for which the graph has points.

   **Range in Set-Builder Notation:**
   \[
   \{ y \mid -2 \leq y \leq 5 \}
   \]
   The graph extends vertically from \( y = -2 \) to \( y = 5 \).

### 3. **Is the graph a function?**
   A graph represents a function if, for every \( x \)-value, there is at most one corresponding \( y \)-value. In other words, it must pass the vertical line test.

   **Answer:**
   **No**, the graph is not a function, because there are \( x \)-values where a vertical line would intersect the graph at more than one point (e.g., at \( x = -1 \)).

Would you like more details or have any questions?

### Related Questions:
1. How do you determine the domain of more complex graphs?
2. What methods can be used to determine if a graph is a function?
3. How would the domain and range change if the triangle were moved upward?
4. What is the significance of the range in real-world applications?
5. Can a shape with curves, like a circle, be a function?

### Tip:
Always check if the graph passes the vertical line test to determine if it represents a function.

Understand how to analyze the domain, range, and determine if a graph represents a function using set builder notation. This problem involves identifying the inputs and outputs of a graph and applying the vertical line test. Suitable for high school students learning about functions and set theory.

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