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The image you've uploaded contains a set of graph-based questions, focusing on domains, ranges, and functions. I'll analyze the graphs shown and provide insights into each problem depicted.

### Observations and Solutions:

1. **Top Graph (Problem 5)**:
   - **Graph**: A horizontal line from \( x = 2 \) to \( x = 7 \).
   - **Domain**: \( [2, 7] \) - This indicates the graph exists only from \( x = 2 \) to \( x = 7 \).
   - **Range**: \( \{4\} \) - The line stays constant at \( y = 4 \), so the range is just this single value.
   - **Type**: This is **not a function** because a vertical line at any \( x \)-value between 2 and 7 will intersect the graph more than once, violating the vertical line test.

2. **Middle Graph (Problem 6)**:
   - **Graph**: A horizontal arrow starting from \( x = 6 \) and extending to the left indefinitely.
   - **Domain**: \( (-\infty, 6] \) - The graph covers all \( x \)-values up to and including 6.
   - **Range**: \( \{5\} \) - The line is at a constant \( y = 5 \), so the range is just 5.
   - **Type**: This is a **function** because it passes the vertical line test everywhere.

3. **Bottom Graph (Problem 7)**:
   - **Graph**: A diagonal line extending through all quadrants.
   - **Domain**: \( (-\infty, \infty) \) - This line extends infinitely in both directions, so the domain is all real numbers.
   - **Range**: \( (-\infty, \infty) \) - Since the line spans all \( y \)-values, the range is also all real numbers.
   - **Type**: This is a **function** because it passes the vertical line test everywhere.

Would you like more details or explanations on any of these problems? Here are some related questions you might find helpful:

1. What is the significance of the vertical line test in determining functions?
2. How do you determine the domain and range for a graph that is not a straight line?
3. Can a function have a domain or range that includes negative infinity or positive infinity?
4. What are some real-life applications where determining the domain and range of a function is crucial?
5. How do piecewise functions differ in terms of domain and range from regular functions?

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

Explore detailed solutions to graph-based math problems focusing on domains, ranges, and functions. Understand the significance of the vertical line test and how to determine domains and ranges for different graph types.

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