The function f (x) = cube root of x is an example of a logarithmic function.

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This is a false statement.

The cube root of x also means x raised to the 1/3rd power. In order for it to be a logarithmic function, it needs to grow as a inverse to a power function. Since we still have a number raised to a power (albeit a very low power) it is not a logarithmic function.

All logarithmic functions will approach the y axis as they get lower and lower. The cube root of x will actually hit the y-axis at (0, 0)