Slant Asymptotes

A slant asymptote is a non-horizontal and non-vertical line which graph of a function will approach, yet never cross. Slant asymptotes occur in rational functions where the degree of the numerator function is exactly one more than the degree of the denominator function. In the graph below, is the numerator function and is the denominator function. The blue function being graphed is . The dotted red line is the slant asymptote of .
Type in different polynomial functions for and .
  1. What conditions must be true for to have a slant asymptote?
  2. With the conditions above fulfilled, use long division to divide .
  3. How do your results compare to the slant asymptote of ?