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

1 Answer
May 6, 2016

Answer:

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,
#color(red)("the degree in the numerator " >" the degree in the denominator")#
There are #color(red)("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.
enter image source here
The quotient is the oblique asymptote.
Therefore, the oblique asymptote for the given function is #y=x-2#.