How do you find the slant asymptote of #(x^2+3x-4)/x#?
Divide the expressions and discard the remainder.
Ok, so the slant asymptote means that as x gets infinitely big, the graph gets closer to a particular line, which is the slant asymptote. So you divide the numerator by the denominator, and, assuming it's (
In this case you can divide all numerator terms by x, so
Please note that slant asymptotes only occur when the degree (highest exponent) in the numerator is exactly one more than the denominator, in this case 2 & 1. Also note that in a more complicated case, as if you had say (x+1) in the denominator, then you'd have to use long or synthetic division to get the asymptote.