# Thread: Domain and range

1. ## Domain and range

What is the difference between domain and range? Describe a real life situation that could be modeled by a function.

Thank You

2. Originally Posted by OneidaFL
What is the difference between domain and range? Describe a real life situation that could be modeled by a function.

Thank You
Domain is the set of values for which a function is defined. Range is a set of values that the output of a function is restricted to.

For example, a function that calculates sales tax. The domain is usually positive numbers with at most two decimal places of precision, although for getting gas (at least here in the United States) an extra decimal place of precision is usually added, as maybe in other cases too. The range can actually be any set, as long as it contains all the values that the function can output. So we can let the range be the set of all real numbers, or the set of all complex numbers, or the set of all rationals, or (most restrictively) the set of nonnegative numbers with at most two decimal places of precision.

I suppose one could argue that 0 is also a valid input for the function, returning 0. It's up to preference, I'd say.

3. A note on what I wrote above: in a strict sense, the example function I gave above isn't an example of modeling, because it doesn't take a complex situation and reduce it to a simpler model.

So, you could take a function that models population growth. Domain could be nonnegative real numbers indicating time since initial time. Range could be all reals (0 means no growth, positive means growth, negative means decay).