Graphing Rational Functions Dr. Jason Gershman

Horizontal Asymptotes If the degree of the denominator is greater than the degree of the numerator, you will have a horizontal asymptote at y=0 If the degrees are the same you will have a horizontal asymptote at y equal to a value which is the ratio of the leading coefficients of the numerator and denominator.

Slant Asymptotes If the degree of the numerator is exactly one degree greater than the degree of the denominator, you will have a slant asymptote of the for y=mx+b which is found via long division (tossing aside the remainder.) Non-linear asymptotes are obtained when the degree of the numerator is two or more degrees larger than the degree of the denominator.

Vertical Asymptotes Vertical asymptotes occur at value x=c where c is a value is causes the denominator to be 0 and which cannot be removed by factoring (if it can be cancelled with a term in the numerator, it creates a hole in the graph.)

Effects of Changing Coefficients Change the values and the signs of the leading coefficients to see how the graph of the rational function changes. gebra2/9-1.htm What do you conclude in general?

Real Zeros Also called real roots of the rational function These are values which make the numerator 0 but do not make the denominator 0. If the degree of the numerator is m, then the rational function has at most m real roots. Be careful of holes in the graph.

Practice Practice looking at the effects of changing coefficients in a more complex setting to see how this effects the number of real roots and the types of and number of asymptotes. enu/GeogebraFiles/rationalfunc/ratfuncgerma ntrans.html

Review of Objectives We’re simplifying complex functions and graphing them. Why is this important? What can this be related to in a student’s daily life?