# How do you find the vertex for the function f(x)=1/x?

This hyperbola can be written $x y = 1$, which is symmetric in $x$ and $y$, so the vertices must lie on the line $y = x$, that is at $\left(1 , 1\right)$ and $\left(- 1 , - 1\right)$
The line $y = x$ intersects $y = \frac{1}{x}$ at the points $\left(- 1 , - 1\right)$ and $\left(1 , 1\right)$, where both equations are satisfied.