I take this to be r(t)=(t-3)/(t+8). The domain is the range of values of t for which the function can be evaluated. This function cannot be evaluated when the denominator is zero, that is, when t=-8. So the domain is all values of t except the single value t=-8. When t is slightly above or below this value r(t) is very large and positive (<-8) or very large and negative (>-8).