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

Mar 31, 2016

$f \left(x\right) = \frac{x + 1}{x - 1}$
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) = $\frac{1001}{999} \approx 1.002$ and subsequently larger numbers will produce numbers even closer to 1.
• There is no slant asymptote since there is a horizontal asymptote.

See graph: