Write the rational function. Rational functions are fractions with a denominator. Suppose it is given by y = (x+1)/(x-1).
Set the denominator equal to zero and solve to find the vertical asymptote of the function. In this example, the denominator is given by (x-1) and the solution to x -1 = 0 occurs when x = 1. Remember that there can be multiple solutions if the denominator is quadratic or higher powered.
Determine the limits of the function as the denominator approaches the asymptote from the left and from the right. In this case, note that as x approaches 1 from the left--that is, from slightly less than 1 to towards 1 ---the function tends to negative infinity. Approaching from the right, the function tends to positive infinity as it nears 1.
Mark discontinuity from negative to positive infinity at the vertical asymptote with steep, curved, near-vertical ("asymptotic") lines.
Graph the vertical asymptote found in Step 2 using a dotted line. The dotted line denotes that that the function is undefined at that value of x. In this case, draw a straight, dotted line at x =1.