# How do you find the vertical, horizontal or slant asymptotes for  y = 4/(x - 3)?

Feb 12, 2017

The vertical asymptote is $x = 3$
The horizontal asymptote is $y = 0$
No slant asymptote

#### Explanation:

As you cannot divide by $0$, $x \ne 3$

The vertical asymptote is $x = 3$

The degree of the numerator is $<$ than the degree of the denominator, there is no slant asymptote.

${\lim}_{x \to - \infty} y = {\lim}_{x \to - \infty} \frac{4}{x} = {0}^{-}$

${\lim}_{x \to + \infty} y = {\lim}_{x \to + \infty} \frac{4}{x} = {0}^{+}$

The horizontal asymptote is $y = 0$

graph{(y-(4/(x-3)))(y)(y-300x+800)=0 [-11.25, 11.245, -5.63, 5.62]}