What is the range of the function f(x) = 5/(x-3)?

Jan 8, 2017

The range of $f \left(x\right)$ is ${R}_{f} \left(x\right) = \mathbb{R} - \left\{0\right\}$

Explanation:

The domain of $f \left(x\right)$ is ${D}_{f} \left(x\right) = \mathbb{R} - \left\{3\right\}$

To determine the range, we calculate the limit of $f \left(x\right)$ as $x \to \pm \infty$

${\lim}_{x \to - \infty} f \left(x\right) = {\lim}_{x \to - \infty} \frac{5}{x} = {0}^{-}$

${\lim}_{x \to + \infty} f \left(x\right) = {\lim}_{x \to + \infty} \frac{5}{x} = {0}^{+}$

Therefore the range of $f \left(x\right)$ is ${R}_{f} \left(x\right) = \mathbb{R} - \left\{0\right\}$

graph{5/(x-3) [-18.02, 18.01, -9, 9.02]}