# How do you find the vertical, horizontal or slant asymptotes for f(x) = (x^2 - 2x + 1)/(x)?

May 6, 2016

Vertical asymptote is $x = 0$

No horizontal asymptote

Oblique asymptotes is $y = x - 2$

#### Explanation:

An ASYMPTOTE is a line that approches a curve, but NEVER meets it.

To find the vertical asymptote , put the denominator = 0 (because 0 cannot divide any number) and solve.

Here, $x = 0$

The curve will never touch the line $x = 0$ or the $y$-axis, thereby making it the vertical asymptote.

Next, we find the horizontal asymptote:
Compare the degree of the expressions in the numerator and the denominator.
Since,
$\textcolor{red}{\text{the degree in the numerator " >" the degree in the denominator}}$
There are $\textcolor{red}{\text{no horizontal asymptote}}$.

The oblique asymptote is a line of the form y = mx + c.
Oblique asymtote exists when the degree of numerator = degree of denominator + 1

To find the oblique asymptote divide the numerator by the denominator.

The quotient is the oblique asymptote.
Therefore, the oblique asymptote for the given function is $y = x - 2$.