Identifying Asymptotes of a Hyperbola

basic hyperbolic functionHow would I find the vertical and horizontal asymptotes of a $y=\frac{1}{x}$ function algebraically? For example, $y=-\frac{2}{x+3}-1$ (as you would type into a calculator). Simply, how do I find the x and y values by looking at this equation? In other words, the middle point where the asymptotes in the picture has moved and the whole graph has been vertically stretched, where are the asymptotes now?

basic hyperbolic functionHow would I find the vertical and horizontal asymptotes of a $y=\frac{1}{x}$ function algebraically? For example, $y=-\frac{2}{x+3}-1$ (as you would type into a calculator). Simply, how do I find the x and y values by looking at this equation? In other words, the middle point where the asymptotes in the picture has moved and the whole graph has been vertically stretched, where are the asymptotes now?