The conditions of when a graph has a vertical asymptote and a hole is when the degree of the denominator is greater than the numerator. A hole is when something cancels from both the numerator and the denominator from the factors. When there is a hole, there is a asymptote and an x-intercept that divide the graph into two sections (though they may look connected they are not). Usually the horizontal asymptote has two x-intercepts which divides the graph into three sections instead of two, but there is only two sections when there is a hole.
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