# What is the range of the function x^3 - 5?

Sep 22, 2017

$\left\{y \in \mathbb{R} | - \infty < y < \infty\right\}$

or in interval notation:

$\left(- \infty , \infty\right)$

#### Explanation:

The function is continuous so is valid for all $x$ in $\mathbb{R}$.

So:

as $x \to - \infty$

${x}^{3} - 5 \to - \infty$

as $x \to \infty$

${x}^{3} - 5 \to \infty$

So the range is:

$\left\{y \in \mathbb{R} | - \infty < y < \infty\right\}$

or in interval notation:

$\left(- \infty , \infty\right)$

See graph:

graph{x^3 -5 [-10, 10, -20, 20]}