I think both 1 and 2 cannot be true. Can anyone explain to me why 1 is true?
If $r(x)$ is a rational function, then which of the following cannot be true? 1. The graph of $r(x)$ has a hole in the graph 2. The graph of $r(x)$ has a horizontal asymptote on the left but not on the right
I am not sure what you mean with statement 2 (what is "on the left"? what is "on the right?") but statement 1 is not necessarily false.
For example, consider the function $f(x)=\frac{(x+3)^2}{x+3}$. The graph of $f(x)$ is very similar to the graph of $g(x)=x+3$, but with a "hole" at $x=-3$. This is because when $x=-3$ we have $f(x)=\frac{0^2}{0}$ which is undefined because the denominator is $0$.
Hope this helps!
It is not that 1 is true, it can be false (look no furter than 1/x, which, by the way, has an asymptote, not a hole, which is best to think of as a single missing point rather than a huge jump between infinities.).
The correct answer you may be reading, is that 2 is always false.