# How do you graph and find the discontinuities of f(x) = 1/x ?

Aug 17, 2015

The most obvious discontinuity is when $x = 0$ because that is not defined.

#### Explanation:

If $x \to 0$ from positive, $f \left(x\right)$ will grow, or in the "language":
${\lim}_{x \to {0}^{+}} f \left(x\right) = \infty$

Almost he same goes for $x \to 0$ from negative:
${\lim}_{x \to {0}^{-}} f \left(x\right) = - \infty$

If $x$ gets greater and greater (both positive and negative) $f \left(x\right)$ will be smaller and smaller, without actually reaching $0$, or:
${\lim}_{x \to \infty} f \left(x\right) = {\lim}_{x \to - \infty} f \left(x\right) = 0$

$x = 0 \mathmr{and} y = 0$ are called the asymptotes.
graph{1/x [-10, 10, -5, 5]}
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