How do you find vertical, horizontal and oblique asymptotes for #(x^2-9x+4)/(x+6)#?

1 Answer
May 31, 2016

Answer:

The vertical asymptote as at #" "x=-6#
The oblique asymptote is #" "y=x-15#

Explanation:

Given:#" "(x^2-9x+4)/(x+6)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Determine the vertical asymptote")#

The equation is undefined at the denominator being 0

So the excluded value is that which gives #1+6= 0#

#color(green)("So the vertical asymptote as at "x=-6)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)("Determine the oblique asymptote")#

Investigate the extreme values of #x#

#color(brown)("I can not spot how to simplify the given expression so by")#
#color(brown)("polynomial division we have "y= x-15+94/(x+6))#

#y=lim_(x->color(white)()^(-)oo ) x-15+94/(x+6)" "=" "x-15#

#color(green)("So the oblique asymptote is "y=x-15)#

Tony B