How do you find the slant asymptote of #y = (x^2 -3x +2) / (x - 4)#?

1 Answer
Jan 15, 2016

Answer:

#y=x+1#

Explanation:

#(x^2-3x+2)div (x-4) = color(green)((x+1)) # plus an irrelevant constant remainder
graph{(y-(x^2-3x+2)/(x-4))(y-(x+1))=0 [-22.8, 28.53, -10.58, 15.06]}

If #y=f(x)/g(x)# where #f(x)# and #g(x)# are both polynomial functions
#color(white)("XXX")#and #"degree"(f(x)) > "degree"(g(x))#
then (disregarding any remainder)
#color(white)("XXX")#the oblique (or "slant") asymptote is given by the equation
#color(white)("XXXXXX")y=f(x)/(g(x)#