How To: Find the vertical asymptotes of rational functions

To find a vertical asymptote, you are trying to find values of x that produce 0 in the denominator but not in the numerator. If 0/0 occurs, that means you have a "hole" in the graph. A vertical asymptote is a place in the graph of infinite discontinuity, where the graph spikes off to positive or negative infinity. To find the vertical asymptote, set the denominator equal to zero and solve for x. Check that the values also do not give a zero in the nominator. If the values work, you have found the vertical asymptote(s). Several examples illustrate and clarify the principles.