Question

Function discontinuities.
http://imgur.com/zob96

Answer 1

use the limits

Answer 2

if the limit from left and right are equal to the function then it is continuous

Answer 3

First of all the left and right limit of the function must be same at x=0 and x=1, this gives us for x=0:
\[ 0^2-a = \frac{-2}{0+b} \Leftrightarrow a = \frac{2}{b} \]
and for x = 1:
\[ \frac{-2}{1+b} = a*1-3 \Leftrightarrow a = \frac{-2}{1+b}+3 \]
Put together:
\[ \frac{-2}{1+b}+3 = \frac{2}{b} \]
The solution of this yields 2 solutions, b=1 or b=-2/3 with a=2 or a=-3, respectively.