# How do you determine where the function is increasing or decreasing, and determine where relative maxima and minima occur for f(x) = (x - 1)/x?

If we want to know everything about $f$, we need $f '$.
Here, $f ' \left(x\right) = \frac{x - x + 1}{x} ^ 2 = \frac{1}{x} ^ 2$. This function is always strictly positive on $\mathbb{R}$ without $0$ so your function is strictly increasing on ]-oo,0[ and strictly growing on ]0,+oo[.
It does have a minima on ]-oo,0[, it's $1$ (even though it doesn't reach this value) and it has a maxima on ]0,+oo[, it's also $1$.