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What is the domain and range of a function (in general terms)?

What is the domain and range of a function (in general terms)? Why do units of
time, distance and money often restrict the domain of a real-world model to only
positive values of the input?

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2 Answers

Depending on the level of math in which this question is answered, there is a slightly more-general but more-tripup answer. I'm going to assume you are not currently studying abstract algebra / group theory, however.

Sometimes "range" can be used to describe a general overview of what kind of results a function can get you. Consider a formula like

d = s*t

Not knowing the context of what the symbols mean, we can just say that in the real world d, s, and t are all real numbers. The domain is the real numbers, and multiplying them also gives real numbers, which is the range.

But let's rephrase the formula:

distance = speed * time

Well, in the real world again, there is no negative distance, nor is there negative speed, nor is there negative time. So with that little bit more information, we want to rephrase things: our domain is the positive real numbers, and our range is the positive real numbers.

One more:

e = v^2

Once again, knowing nothing, v is any real number and so is e. But what if we want e to be negative? There is no real number that v can be that will make v^2 negative. So while we can put in whatever we want for v, we can only get positive results for e: "The domain of e is all real numbers; the range of e is all non-negative (positive or 0) real numbers."

I hope this answer is appropriate for your grade level.


Domain is the possible values that can be plugged into a formula.

Range is the possible output values that can be produced by a formula.

Time, distance, and money are often restricted to positive values of input because of what negative values would means.

Negative time requires going into the past.

Negative distance means being closer to the starting point than the point is to itself.

Negative money means going into debt or having the customer give the product while the supplier is paying the money.