# What is the domain and range of f(x) = x^3 + 5?

Aug 4, 2015

Domain: $\left(- \infty , + \infty\right)$
Range: $\left(- \infty , + \infty\right)$

#### Explanation:

Your function is defined for any value of $x \in \mathbb{R}$, so you have no restrictions on its domain $\to$ its domain is $\left(- \infty , + \infty\right)$.

The same can be said for its range. The function can take any value in the interval $\left(- \infty , + \infty\right)$.

graph{x^3 + 5 [-8.9, 8.88, -4.396, 4.496]}

Aug 4, 2015

Domain and range of $f \left(x\right) = {x}^{3} + 5$

#### Explanation:

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

Domain: (-infinity, +infinity)
Range (-infinity, +infinity)