Rational Functions

1. Oblique Asymptotes

1.1. If the degree of the numerator is greater than the degree of the denominator by one, there is an oblique asymptote. The asymptote is the quotient numerator divided by the denominator.

2. X- Intercepts

2.1. To find the x intercepts you equal the whole function to zero and then solve for x

3. Y- Intercepts

3.1. To find the y intercepts you substitute the x values for zeroes and then solve for f(x)

4. Vertical asymptotes

4.1. They are found using the zeroes of the denominator

5. Horizontal Asymptotes

5.1. If the degree of the numerator is bigger than the degree of the denominator by more than one, the graph has no horizontal asymptote

5.2. If the degree of the numerator is equal to the degree of the denominator, the horizontal asymptote is the ratio of the two leading coefficients

5.3. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is zero.

6. Holes

6.1. Holes are found when there is the same factor in the numerator as in the denominator