1. Module 4.4 Proper and Improper Rational Functions

2. Proper vs. Improper Rational Functions  Proper Rational Functions: When the degree of the numerator is less than the degree of the denominator.  Improper Rational Functions: When the degree of the numerator is greater than or equal to the degree of the denominator.  Division is possible

3. Simplifying Improper Rational Functions with Long Division  Point to remember, always have to keep place values with variable. If any exponents are missing, add them back in with a 0 coefficient  Multiply everything in the divisor by a value so that the first term is equal to the first term in the dividend.  Subtract the multiplied value from the dividend  Repeat until there are no more terms left.  Write the answer as a polynomial ± the remainder over the divisor

4. Slant Asymptotes  A rational function has a slant asymptote, if the degree of the numerator is exactly one more than the degree of the denominator.  Use division (long or synthetic) to divide the function.  Set the non-remainder portion (should be liner) of the answer equal to y, and that is the equation of the slant asymptote.