Answer
Vertical asymptote: $x=1$
Horizontal asymptote: $y=-1$
Work Step by Step
An asymptote is a line that has the property that as $x$ or $y$ gets large, the distance between the graph and the line approaches zero.
In the graph, you can see that the asymptotes are already labeled in a black dashed line, and you can see that the graph will get closer but never touch the lines. Therefore, you can just see that the lines $y = -1$ and $ x = 1$ are the asymptotes because they are the equations of the black dashed lines.