Final answer:
After doing algebra in rational functions, a hole is where a factor cancels out and the graph is defined nearby, whereas a vertical asymptote is where the denominator equals zero and the graph approaches infinity; thus, the answer is 1) Hole, VA.
Step-by-step explanation:
The question is asking about the difference between a "hole" and a "vertical asymptote (VA)" in the context of graphing rational functions in algebra. A hole in a graph occurs where a factor in the denominator and numerator of a rational expression cancel out; the function is not defined at that specific value, but it can be simplified, and the graph will approach and pass through every other point normally.
On the other hand, a vertical asymptote happens at a value that makes the denominator zero after the function has been simplified fully; the function cannot be simplified to remove this #/0 situation, and the graph will not touch the value but instead approach infinity as it nears.
Thus, the answer to the student's question is that after doing algebra, a hole factors out completely, while a vertical asymptote does not exist and makes #/0. Therefore, the correct answer is 1) Hole, VA.