Strategy For Graphing Polynomials And Rational Functions п‚ п‚ 1. State the domain. 2. Find the Y-Intercept (x=0) and the XIntercept (y=0) the easy ones in particular. вЂ“ You can use the synthetic division to find the easy zeros for the given polynomial function. п‚ п‚ п‚ 3. For rational functions ONLY, find the asymptotes. 4. Find dy/dx and perform the sign analysis. 5. Graph the function. Asymptotes For Rational Functions вЂў 1. Vertical Asymptote: Whatever makes the denominator zero is your vertical asymptote as long as you do not have 0/0. Remember 0/0 means that you have a hole in the graph. вЂў 2. Horizontal And Slant Asymptote: Is the limit of the rational function as xп‚®п‚Ґ Horizontal & Slant Asymptotes п‚ Consider the following rational function: f ( x) пЂЅ п‚ n пЂ1 an x n пЂ« a n пЂ1 x bm x m пЂ« b m пЂ1 x m пЂ1 пЂ« ... пЂ« a 1 x пЂ« a 0 пЂ« ... пЂ« b1 x пЂ« b 0 If the power of the numerator is the same as the power of the denominator, (n=m) then the horizontal asymptote is y = the ratio of the leading coefficients, y пЂЅ an bm п‚ If the power of the numerator is less than the power of the denominator (n<m), then the horizontal asymptote is y=0. п‚ If the power of the numerator is greater than the power of the denominator by one degree (n=m+1), then the slant asymptote is y = the quotient of the division. Here the synthetic division can prove useful. п‚ п‚ Notice that for rational functions you can not have horizontal and slant asymptotes at the same time.