Calculus
posted by Michelle .
The following information is given,
f(x) = 2+x x<(less than or equal to) 3
f(x) = x^2 x > 3 , x < 1
f(x) = 6 1 < (less than or equal to) x
I graphed it, but i don't know how to find the domain and range.

The domain is the allowed values of x (excluding the non allowed).
The range is the value of f(x), which you compute from x.
I will be happy to critique your thinking. 
for f(x) = 2+x : Domain: (negative infinity to 3]
Range: (infinity to 1]
f(x) = x^2 : Domain: (3,1)
Range: (9,1)
f(x) = 6 : Domain: [3,1]
Range: [6]
i don't know how to put them all together though. is this right? 
on the second, the domain does not include 1 nor 3, you have to be careful on the nonincluded points. Same on the range, you can list it as 9e,1+e where e is epsilion.
For an all together ,
domain: neginf to +inf
range: neginf to 9, excluding 1+e to 1 (check that).
There is an assortment of the ways you can describe this. 
That assortment could include notations such as set builder and interval.