# How do you find the domain and range of  f(x)=x^3?

Mar 14, 2017

Domain: $\mathbb{R}$
Range: $\mathbb{R}$

#### Explanation:

To find the domain of the function, find what numbers cause the function to not exist. For example, in the function $f \left(x\right) = \sqrt{x}$, the domain is only non-negative numbers, since you can't take the square root of a negative. However, in this instance, you can cube of any number, so the domain is all real numbers.
Similarly, the range is the numbers that the function can produce. In this function, the range is all real numbers as well, since it can produce any number (given the right input).

You could also look at the graph:
graph{x^3 [-10, 10, -5, 5]}
You can see it continues forever in both the x and y directions, and thus doesn't have an restrictions on its domain or range.