The Cube Root Function: Graph, Domain, Range And Properties

Graph of Cube root function

f(x) = | x |

The cube root function is a special type of radical function that has the general form of f(x) = ∛x. The graph of the cube root function is shown below:


The domain of the cube root function is all real numbers since we can take the cube root of any real number. The range of the cube root function is also all real numbers since the cube root of any real number can be positive, negative, or zero.

The graph of the cube root function has a distinctive shape similar to the letter S. As the input values (x) increase, the output values (y) also increase, but at a slower rate. For example, the cube root of 8 is 2, the cube root of 27 is 3, and the cube root of 64 is 4. Therefore, the function grows more slowly than a linear function but faster than a logarithmic function.

The cube root function has a horizontal asymptote of y = 0 as the values of x approach negative infinity and positive infinity. Also, the cube root function is an odd function, which means that it is symmetric about the origin (0,0).

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