Which statement about the cube root function y = ∛x is true?

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Multiple Choice

Which statement about the cube root function y = ∛x is true?

Explanation:
Every real number has a real cube root, so the cube root function is defined for all real x. The graph is an increasing curve, not a straight line, so the slope is not constant across its domain. In fact, as x approaches zero, the slope becomes arbitrarily large in magnitude, giving a vertical tangent at x = 0, even though the function value at 0 is 0. So the statement that it is defined for all real x is true, while the others don’t fit: it isn’t a line with constant slope, it isn’t undefined at x = 0, and there is no restricted domain.

Every real number has a real cube root, so the cube root function is defined for all real x. The graph is an increasing curve, not a straight line, so the slope is not constant across its domain. In fact, as x approaches zero, the slope becomes arbitrarily large in magnitude, giving a vertical tangent at x = 0, even though the function value at 0 is 0. So the statement that it is defined for all real x is true, while the others don’t fit: it isn’t a line with constant slope, it isn’t undefined at x = 0, and there is no restricted domain.

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