Question
Which relation is a function? (A) \( (1,0),(3,0),(1,1),(3,1)(1,3) \)
Ask by Garrett Bartlett. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The relation is not a function because some inputs are paired with multiple outputs.
Solution
To determine whether a relation is a function, we must verify that **each input** (the first element of each ordered pair) is associated with **exactly one output** (the second element of each ordered pair).
Let's examine the given relation:
\[
(1,0),\ (3,0),\ (1,1),\ (3,1),\ (1,3)
\]
- **Input 1** is associated with three different outputs: **0**, **1**, and **3**.
- **Input 3** is associated with two different outputs: **0** and **1**.
Since **input 1** and **input 3** each map to multiple outputs, this violates the definition of a function, where each input must map to **exactly one output**.
**Conclusion:**
The given relation **is not** a function because some inputs are associated with multiple outputs.
Answer: **A) is not a function because some inputs are paired with multiple outputs.**
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
In a relation, each input (or x-coordinate) must be associated with exactly one output (or y-coordinate) for it to qualify as a function. In the provided relation \( (1,0),(3,0),(1,1),(3,1),(1,3) \), the input value \( 1 \) corresponds to three different outputs: \( 0, 1, \) and \( 3 \). This violates the definition of a function, making it clear that this relation is not a function. To understand this better, consider that for a relation to be a function, every x-value must be linked to one and only one y-value. In simpler terms, if you think of x-values as people making decisions, each of them should only make one decision to keep things clear and organized!
