Determine if the relation is a function: {(1, 2), (3, 4), (1, 5)}

To determine if a given relation is a function, we need to verify if each input (or first element of the ordered pairs) maps to exactly one output (or second element). In other words, no input can be paired with more than one output.

The given relation is:
\[
\{(1, 2), (3, 4), (1, 5)\}
\]

- The input \(1\) is paired with both \(2\) and \(5\).
- The input \(3\) is paired with \(4\).

Since the input \(1\) is associated with two different outputs (\(2\) and \(5\)), this relation is **not** a function. In a function, an input can only be associated with one output.

Would you like more details or have any questions about this? Here are five related questions to expand on this concept:

1. What is the formal definition of a function?
2. How can we represent functions using function notation?
3. How do you determine the domain and range of a function?
4. Can a relation with the same outputs but different inputs be a function?
5. What is the difference between one-to-one functions and general functions?

**Tip:** In a function, each input must have exactly one corresponding output, but multiple inputs can share the same output.

Learn how to determine if a relation is a function using the example {(1, 2), (3, 4), (1, 5)}. Understand the concept of functions, where each input must have exactly one output. Suitable for students in Grades 8-10.

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