Is My Relation a Function? Understanding Input and Output

To determine whether a relation is a function, we need to examine the pairs of input and output values. A relation is defined as a function when every input (x-value) corresponds to exactly one output (f(x)). It’s important to note that having multiple inputs resulting in the same output does not disqualify a relation from being a function.

Let's analyze the pairs you provided: 3 → 2, 0 → 1, 5 → -7, and -3 → 2. In this case, each x-value is unique: 3, 0, 5, and -3 do not repeat. Therefore, despite the fact that two different inputs (3 and -3) yield the same output of 2, this does not violate the definition of a function. What matters is that each input has only one corresponding output.

For further clarity, let’s consider a real-world example. Imagine a vending machine where you enter a number (input) to receive a specific drink (output). If you press button number 1, you’ll always get a soda, and if you press button number 2, you’ll always get water. If multiple buttons can give you the same drink (like button 1 and button 3 both giving soda), this is still a function because each button (input) leads to one specific drink (output).

In summary, the crucial point to remember is that a function can have multiple inputs sharing the same output, but each input must map to only one output. To solidify your understanding, consider practicing with more examples of relations and testing whether they are functions by following these rules. Check the equations section for a formal definition of functions and additional examples to enhance your learning experience.