Question
Is this relation a function? \( \{(-3,-8),(3,-5),(9,-1),(4,-9)\} \) \( \square \) Yes No
Ask by Davey Weaver. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The relation is a function.
Solution
Yes, the given relation is a **function**.
**Reasoning:**
A **function** is a relation in which each input (the first element of each ordered pair) is associated with exactly one output (the second element).
Let's examine the provided relation:
\[
\{(-3, -8),\ (3, -5),\ (9, -1),\ (4, -9)\}
\]
- **Input \(-3\)** is paired with output \(-8\).
- **Input \(3\)** is paired with output \(-5\).
- **Input \(9\)** is paired with output \(-1\).
- **Input \(4\)** is paired with output \(-9\).
Each input value is unique and is associated with only one output value. There are no repeated input values with different outputs. Therefore, this relation satisfies the definition of a function.
**Answer:**
☑ **Yes**
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
Yes, this relation is a function! In a function, each input (or x-value) must correspond to exactly one output (or y-value). Here, the x-values are -3, 3, 9, and 4, and each one is unique, meaning there's no repetition in the x-values connected to multiple y-values. To further explore functions, consider how they form the foundation of many concepts in math and science. They can describe everything from the trajectory of a thrown ball to the growth of a population over time. Delving into how these relationships manifest in real-life scenarios can make learning about them even more exciting!
