# Function| Domain & Range

Suppose that A={0,1,2,3,4}, B={2,3,4,5}, f={(0,3),(1,3),(2,4),(3,2),(4,2)}

Find the domain and range of f. f(1)=? f(2)=?

My opinion is; f(1)=3 and f(2)=4

If I am right, what would be f(2) if there was also (2,3) in f? Edit: I read the definition of a function and I understand that (2,3) cannot be in f. Because, if it was, f would not be a function.

And my opinion is; the domain is {0,1,2,3,4} and the range is {2,3,4}

Finally, is codomain and range are the same thing?

Thank you :)

You are right about what $f (2)$ and $f (1)$ equal. The range is ${2,3,4}$. If there was a $(2,3)$ also, $f$ wouldn't be a function. And yes codomain is the same as range.
• @AYARcom It'a not a line no. And the way it is define above, $f(10)$ doesn't exist because 10 is not apart of the domain you defined above, a.k.a $A$. If you mean $\mathbb {Z}$, as in integers, the whole integers is not the domain and range. The function is not continuous it has a domain ${0,1,2,3,4 }$ and range ${2,3,4}$. The function is discrete. It only exists for what you defined above. Aug 31 '14 at 20:48
• @AYARcom Oh, makes sense why I was confused. Yes $\mathbb {Z}$ is the domain and range of the function you just stated. Aug 31 '14 at 22:21