Let's analyze the questions provided in the image:

13. Identify the domain and range of the relation. Is the relation a function? Explain.

• Domain: The x-values are {5, 8, 10, 12, 14}.
• Range: The y-values are {3, 6, 11}.
• Function: No, because one x-value (e.g., 8) is paired with two different y-values (6 and 3), violating the definition of a function.

14. Identify the domain and range of the relation. Is the relation a function? Explain.

• Domain: The cities are {A, B, C, D}.
• Range: The teams are {Rockets, Birds, Pups, Cats, Hawks}.
• Function: No, because one city (e.g., C) is paired with multiple teams (Pups and Cats), violating the definition of a function.

Analyze each situation (15–17):

15. An airplane travels at 565 mph.

• Domain: All non-negative real numbers representing time in hours.
• Range: All non-negative real numbers representing distance.

16. Tickets to a sporting event cost $125 each.

• Domain: Non-negative integers representing the number of tickets.
• Range: Non-negative multiples of 125 (e.g., {0, 125, 250, ...}).

17. An average person consumes 2,000 calories each day.

• Domain: Non-negative integers representing days.
• Range: Non-negative multiples of 2000 (e.g., {0, 2000, 4000, ...}).

Determine whether each relation is a function (18–21):

18. Graph Analysis:

• Not a function. The vertical line test fails because some vertical lines intersect the graph at multiple points.

19. Graph Analysis:

• Function. Passes the vertical line test.
• Not one-to-one, as some horizontal lines intersect the graph at multiple points.

20. Graph Analysis:

• Not a function. The vertical line test fails because some vertical lines intersect the graph at multiple points.

21. Graph Analysis:

• Function. Passes the vertical line test.
• One-to-one, as every horizontal line intersects the graph at most once.

Do you have further questions or need additional clarification? Here are 5 related questions to expand on this material:

1. What makes a relation a function, and how does the vertical line test apply?
2. How do you identify whether a function is one-to-one using a graph?
3. Can a relation be a function if one input maps to multiple outputs?
4. How do domain and range differ in continuous versus discrete scenarios?
5. What real-life examples demonstrate one-to-one functions versus non-one-to-one functions?

Tip: To identify if a graph represents a function, always apply the vertical line test! If any vertical line crosses the graph more than once, it’s not a function.