Unit G #4: Vertical Asymptote vs Hole

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

The difference between a graph having a vertical asymptote and a graph having a hole is the points plotted.  A vertical asymptote and hole are directly related because you find the hole from solving the vertical asymptote.  The vertical asymptote goes up and down.  When solving for the vertical asymptote, you factor the top and bottom, then cross off any common factors.  If you cancelled any factors during the process, these becomes holes (ordered pairs).  The x-value of the ordered pairs is the common factor that was crossed off, and the y value is the number you get when plugging the x-value back into the simplified equation.  These points will be open circles.