How do you identify all asymptotes for #f(x)=(x^2-3x+2)/x#?

1 Answer
Apr 15, 2018

Answer:

See below.

Explanation:

Vertical asymptotes occur where the function is undefined, for:

#(x^2-3x+2)/x#

This is undefined for #x=0# ( division by zero )

Vertical asymptote is the line: #x=0#

Notice that the degree of the numerator is greater than the degree of the denominator. In this case there is an oblique asymptote. This will be a line of the form #y=mx+b#. To find this line, we divide the numerator by the denominator. We only need to divide until we have the equation of a line.

#:.#

Dividing by #x#:

#(x^2/x-3x/x+2/x)/(x/x)=x-3+2/x#

So the oblique asymptote is the line:

#color(blue)(y=x-3)#

The graph confirms these findings:

enter image source here