SOLUTION: find the rational fraction, identify any holes or horizontal or vertical asymptotes of its graph: Y= x+3 / x+3

Algebra ->  Rational-functions -> SOLUTION: find the rational fraction, identify any holes or horizontal or vertical asymptotes of its graph: Y= x+3 / x+3      Log On


   



Question 390350: find the rational fraction, identify any holes or horizontal or vertical asymptotes of its graph:
Y= x+3 / x+3

Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
The function y+=+%28x%2B3%29%2F%28x%2B3%29 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%28x-%3Einfinity%2C+f%28x%29%29+=+c for constant c (c is the horizontal asymptote. Limit may also approach negative infinity.)

In this case,

lim%28x-%3Einfinity%2C+%28x%2B3%29%2F%28x%2B3%29%29+=+1 so 1 is the horizontal asymptote.