# Help with Input and Output relationships?

Here's the question: Give three examples of input-output relationships in real life that cannot have negative values in the practical range? Explain why their range cannot have negative values?

It's a confusing question because how can a relationship have both and input and output?

Could time be a input-output relationship?

• "Input-output relationship" is not a standard mathematical term, so if your teacher is using that, zie should have told you what it was supposed to mean. In mathematics, we speak of things like functions (also called mappings), which I suspect are what you're talking about. We also speak of relations, which are a more abstract/general concept. Commented Nov 7, 2013 at 22:16
• Maybe that's why I'm so confused, Nothing about the question really makes sense to me, How can something have a an "imput-output" relationship? that has a practical range.
– Theo
Commented Nov 7, 2013 at 22:19

To give an example of an input-output relationship, just think about a function.

For instance, suppose $f$ is a function that tracks revenue at a lemonade stand. It takes "number of cups sold" as an input and gives "dollars made" as an output. It might look like this:

$f(x)=.25x$

Assuming that each cup of lemonade costs .25 cents. So if I sell $5$ cups, then I make:

$f(5)=.25(5)=1.25$ dollars. If I sell 20 cups, I make:

$f(10)=.25(10)=2.50$ dollars. In this case, we call $10$ the input and $2.50$ the output. Does that make sense?

Also note: the domain of $f$ in this example is $[0,\infty).$ That is, the input value must be positive, since we can't sell a negative number of cups. The range is also positive, since $.25*(a\,non-negative\,number)$ is always non-negative.

Let me know if you have any questions!

• Thanks so much, your able to make break it down so I can understand it.
– Theo
Commented Nov 8, 2013 at 0:02