The set of ordered pairs (1, 19), (2, 23), (3, 23), (4, 29), (5, 31) represents the number of tickets sold for a fundraiser. a. Make an arrow diagram that represents the relation.... The set of ordered pairs (1, 19), (2, 23), (3, 23), (4, 29), (5, 31) represents the number of tickets sold for a fundraiser. a. Make an arrow diagram that represents the relation. b. Is the relation a function? Explain.
Understand the Problem
The question is asking to create an arrow diagram to represent a set of ordered pairs related to ticket sales and to determine whether this set represents a function, providing an explanation for the answer.
Answer
Yes, the relation is a function.
Answer for screen readers
Yes, the relation is a function.
Steps to Solve
- Identify the Ordered Pairs
The ordered pairs given are:
- (1, 19)
- (2, 23)
- (3, 23)
- (4, 29)
- (5, 31)
Here, the first number in each pair represents the day, and the second number represents the number of tickets sold.
- Create the Arrow Diagram
To create an arrow diagram, we'll represent each day (input values) with arrows pointing to the corresponding number of tickets sold (output values):
- Day 1 (1) → 19
- Day 2 (2) → 23
- Day 3 (3) → 23
- Day 4 (4) → 29
- Day 5 (5) → 31
This would visually show like this:
1 → 19
2 → 23
3 → 23
4 → 29
5 → 31
- Determine if the Relation is a Function
A relation is a function if every input (day) is associated with exactly one output (number of tickets sold).
To check:
- Day 1 has ticket sales of 19.
- Day 2 has ticket sales of 23.
- Day 3 also has ticket sales of 23 (same as Day 2).
- Day 4 has ticket sales of 29.
- Day 5 has ticket sales of 31.
Since the same input of Day 3 corresponds to a repeated output (23), but it's still consistent with a single output for each day, the relation is a function.
- Final Conclusion
The relation forms a function because each day is associated with one distinct output. Even if different days share the same output, it does not break the requirement of a function.
Yes, the relation is a function.
More Information
In a function, each input must map to exactly one output. In this case, even though Day 2 and Day 3 have the same output of 23 tickets sold, each day still has its own distinct input, maintaining the function properties.
Tips
- Confusing a function with a relation: A common mistake is thinking that repeating outputs across different inputs disqualifies a relation as a function. It's essential to check if each input is unique.
- Not properly understanding ordered pairs: Misinterpreting which number represents the input versus the output can lead to incorrect conclusions.
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