Graph of the Reciprocal Function $y = 1/x$

$y = \dfrac{1}{x}$ is undefined at $x = 0$, so both its domain and range are all real numbers except $0$.

As $x \to \pm\infty$ it approaches $0$ (the $x$-axis is an asymptote), and as $x \to 0$ it diverges to $\pm\infty$ (the $y$-axis is an asymptote). It is an odd function, symmetric about the origin, and its graph is a hyperbola lying in the first and third quadrants.