If $r(x)$ is a rational function then which of the following cannot be true?

Question

I don't understand why choice 4) is not a right one. Can anyone explain it to me? What does "has a hole in the graph" mean? Does it mean $y(x)$ is negative infinity?

If $r(x)$ is a rational function then which of the following cannot be true? 1) the graph of r(x) is continuous; 2) the graph of r(x) has a horizontal asymptote on the left and right; 3) the graph of r(x) has a vertical asymptote; 4) the graph of r(x) has a hole in the graph, and 5) the graph of r(x) has a horizontal asymptote on the left but ont on the right.

Answer 1

Depends on what you mean by a "hole" and by a "rational function". The function $r(x) = \frac{x^2}{x}$ could be said to have a "hole" at $x=0$ because $0/0$ is undefined. However, this is a "removable singularity", and one usually identifies this expression with $x = \frac{x}{1}$ which has no "hole".