Question 390350
The function {{{y = (x+3)/(x+3)}}} is equivalent to {{{y = 1}}} except where x = -3 (this is where the hole is). Other than x = -3, the function is constant. You could say that the asymptote is 1, but a horizontal asymptote is usually defined as y "approaching" 1 as x goes to positive or negative infinity. I would still call this an asymptote, as an asymptote is defined if


{{{lim(x->infinity, f(x)) = c}}} for constant c (c is the horizontal asymptote. Limit may also approach negative infinity.)


In this case,


{{{lim(x->infinity, (x+3)/(x+3)) = 1}}} so 1 is the horizontal asymptote.