Which equation represents a cube root function?

• A. y = x^2
• B. y = log x
• C. y = 1/x
• D. y = ∛x

Answer: (D)

Recognize a cube root function by how it undoes cubing. The cube root of x is the number y such that y^3 = x, so the function that gives this output is y = ∛x (or y = x^(1/3)). This function is defined for all real x, passes through the origin, and is odd: ∛(-x) = -∛(x). It grows slowly near zero but increases without bound as x grows, and decreases without bound as x becomes more negative. In contrast, the square function y = x^2 only produces nonnegative values, the logarithm y = log x requires x > 0, and the reciprocal y = 1/x is not defined at x = 0 and has a vertical asymptote. So the equation that represents a cube root function is y = ∛x.