Question

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.

Answer 1

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.

Answer 2

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?

Answer 3

on the second, the domain does not include -1 nor -3, you have to be careful on the non-included points. Same on the range, you can list it as 9-e,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.

Answer 4

That assortment could include notations such as set builder and interval.