How do you find the asymptote(s) of # f(x) = (x+1) / (x+2)#?

Question

Julia Adams · Accepted Answer

For Vertical
Take the denominator and solve for x
#x+2=0#
#x=-2# For horizontal
Try to remember this:
BOBO(bigger on bottom y = 0)
BOTN (bigger on top, none)
EATSDC (exponents are the same, divide constant) Compare the largest exponent on the numerator and denominator to see if it's BOBO, BOTN, or EATSDC The only exponent is #x^1# so your Horizonal asymptote is 1. No oblique asymptote

Jace Anderson · Answer

undefined To find the asymptotes of $ f(x) = \frac{x + 1}{x + 2} $:

1. Identify any vertical asymptotes by determining where the denominator equals zero. In this case, $ x + 2 = 0 $, so $ x = -2 $ is a vertical asymptote.
2. Horizontal asymptotes can be found by examining the behavior of the function as $ x $ approaches positive or negative infinity. Since the degree of the numerator and denominator are the same, the horizontal asymptote is the ratio of the leading coefficients. In this case, it's $ y = 1 $.
3. There are no slant or oblique asymptotes for this rational function.

Avery Alexander · Answer

undefined To find the asymptotes of $ f(x) = \frac{x+1}{x+2} $, set the denominator equal to zero and solve for $ x $. The vertical asymptote occurs where the denominator is zero, so $ x = -2 $ is the vertical asymptote. There is no horizontal asymptote because the degrees of the numerator and denominator are equal.