How do you find the vertical, horizontal or slant asymptotes for #( x + 1)/(x - 1)#?

1 Answer
MrsRudolph221
Mar 31, 2016

#f(x)=(x+1)/(x-1)#
Your vertical asymptote is x = 1, the horizontal asymptote is y = 1, and there are no slant asymptotes.

Explanation:

  • To find the vertical asymptote, set the denominator equal to 0.
  • To find the horizontal asymptote, you can substitute in very large positive and/or negative values for x: f(1000) = #1001/999 ~~1.002# and subsequently larger numbers will produce numbers even closer to 1.
  • There is no slant asymptote since there is a horizontal asymptote.

See graph:mysscreenshot4

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