Unit G Summary Questions #4: Vertical Asymptotes and Holes

4. What is the difference between a graph having a vertical asymptote and a graph having a hole?

When we look at the difference of a graph of a vertical asymptote and a hole we can also look at how it is find. In order to find vertical asymptotes and holes we use the factored equation. Vertical asymptotes are found by setting the denominator equal to zero and putting the result(s) into the equation x=#. We use this equation(s) and are represented on a graph with a dotted line. We find holes by setting the crossed off common factors to zero and plugging the x-value into the simplified equation to get the y-value. With both values we then set it as a point of (x,y) and are plotted with an open circle. A vertical asymptote is a line in a graph while a hole is a point in the graph. Sometimes a graph will only have one or the other.