Question

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

Answer 1

`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)`