# How do you find vertical, horizontal and oblique asymptotes for (x+3)/(x-1)?

Mar 14, 2016

vertical asymptote x = 1
horizontal asymptote y = 1

#### Explanation:

Vertical asymptotes occur as the denominator of a rational function tends to zero. To find the equation let the denominator equal zero.

solve : x - 1 = 0 → x = 1 is the asymptote

Horizontal asymptotes occur as  lim_(x→±∞) f(x) → 0

divide all terms on numerator/ denominator by x

$\frac{x + 3}{x - 1} = \frac{\frac{x}{x} + \frac{3}{x}}{\frac{x}{x} - \frac{1}{x}} = \frac{1 + \frac{3}{x}}{1 - \frac{1}{x}}$

as x → ∞ ,  3/x" and " 1/x → 0

$\Rightarrow \text{ equation of asymptote is } y = 1$

Here is the graph of the function
graph{(x+3)/(x-1) [-10, 10, -5, 5]}