Hey I'm not to sure how to set it up on here, but I'll try my best to make sense of the question,

f(x) = { 3-1/2x if x is less than = 2, 2x-5 if x greater than 2

So I have to find the domain and sketch the graph, this is what I have;

I first thought I was suppose to make 3-1/2x = 0 and isolate x for domain, but I think for these piecewise functions I just plug in the 2 and see what the function equals to and I can get the domain?

f(2) = 3-1/2(2) = 2

f(2) = 2(2)-5 = -1

So the domain is ( - infinity, 2]U(-1, infinity)?

And the graph I believe would be two likes going down first and fourth quadrant, this kind of looks odd to me and I'm not sure what I really did wrong? Thanks.