Continous function with one of ranges as an equation I'm pretty new here and my formatting might have some errors, sorry I could get it only this far.
f(x) =
\begin{cases}
\ ax+2b,  & x<0 \\[3ex]
\ x^2 + 3a -b, & x^2 + 3a -b \\
\ 3x-5,   &  x > 2 \\
\end{cases}
The question here is 
"if following function is continuous for every x, what are the values unknowns a and b  can get?"
I know that for a function to be continuous it has to have a limit and not skip any points etc so "x^2+3a-b" should cover the range between 2 and 0, but I don't know the exact solution nor how do I validate this(if someone has a way of putting this into wolframalpha, please do tell, or even any form of continuity so I can validate my answers)
The method I am most sure about  is for point "0" I can put 0 instead of x and it has to be equal to the second formula, and I can then put "2" instead of "x" in second and third formula and try to get something from there, but I don't know the exact solution nor the answer. 
If someone knows how can I solve this and by doing what I can do the math so I don't expect you guys to solve it completely but I simply don't know the path I should take.
Thanks in advance.

Just as you planned: Plugging 0 for $x$, you'd get $2b = 3a - b$. Plugging 2 for $x$, you'd also get $4 + 3a - b = 1$. Can you take it from here?
