Slant Asymptotes

Consider a rational function whose denominator is of degree 1 or greater.

If the degree of the numerator is exactly one more then the degree of the denominator, the graph of the function has a slant (or oblique) asymptote

For example, the graph of 2

1

x xf x

x

has a slant asymptote.

To find the equation of a slant asymptote, use long division.

As increases or decreases without bound,

2the remainder term approaches 0,

1

so the graph of approaches the line 2.

x

x

f y x