# How do you graph f(x)=(x-1)/(x+1) using holes, vertical and horizontal asymptotes, x and y intercepts?

Apr 25, 2017

Vertical asymptote: $x = - 1$
Horizontal asymptote: $y = 1$
No holes, $x$-intercept $\left(1 , 0\right)$; $y$-intercept $\left(0 , - 1\right)$

#### Explanation:

Rational equation: $f \left(x\right) = \frac{N \left(x\right)}{D \left(x\right)} = \frac{{a}_{n} {x}^{n} + \ldots}{{b}_{m} {x}^{m} + \ldots}$

Find x-intercepts $N \left(x\right) = 0$:
x-1 = 0; x = 1
$x$-intercept $\left(1 , 0\right)$

Find y-intercepts Set $x = 0$:
$f \left(0\right) = - \frac{1}{1} = - 1$
$y$-intercept $\left(0 , - 1\right)$

Find holes:
Holes occur when factors can be cancelled because they are found both in the numerator and denominator. This does not occur in this problem.

Find the vertical asymptotes $D \left(x\right) = 0$:
Vertical asymptotes at x +1 = 0; x = -1

Find horizontal asymptotes When $m = n , y = {a}_{n} / {b}_{m}$:
$m = n = 1$ so there is a horizontal asymptote at $y = 1$

graph{(x-1)/(x+1) [-10, 10, -5, 5]}