The domain of is
equal to the domain of . The range of is equal to the range of . The domain of
is a subset of the real numbers. The range of is a subset of the real
numbers. The domain of is functions from the real numbers to the real
numbers. The range of is functions from the real numbers to the real
numbers.

Two young mathematicians discuss derivatives as functions.

- Devyn
- Riley, I might be a calculus genius.
- Riley
- Yeah? Explain this one to me.
- Devyn
- Let me first ask you a question. Say you have a function, like , and you want to know . Do you plug in the number before or after you find the derivative?
- Riley
- Hmmmm. Well, my next step is usually So I guess before.
- Devyn
- Aha! I think you’re wasting time. You see I write and it means that I
can look at the derivative of my function at
*any*point. So, I plug in the after I’ve found the derivative. - Riley
- That does seem like a pretty genius move. But doesn’t working with , instead of numbers, make all of this more difficult?
- Devyn
- Not at all. Let’s do the problems both ways, at the same time:
- Riley
- Whoa. So now the derivative is a function. Wait, what’s its domain? Its range?

Suppose you have a function . Which of the following are true?