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.