Asymptotes of Reciprocal Functions

If $f = \frac{1}{x-k}$, then the horizontal asymptote of $f$ is at the value $k$.

If $f = \frac{1}{x-k}$, then the vertical asymptote of $f$ is at the value $k$.

If $f = \frac{1 + j}{x}$, then the horizontal asymptote of $f$ is at the value $j$.

If $f = \frac{1 + jx}{x}$, then the horizontal asymptote of $f$ is at the value $j$.

If $f = \frac{\alpha}{x-k} + j$, then the asymptotes are $x = \alpha k$ and $y = \alpha j$.