The graph shows a vertical translation of y = rootindex 3 startroot x endroot.
what is the range of the translated function?
{y|y < 0}
{y|y ≥ 0}
{y|y is a natural number}
{y|y is a real number}

Explanation:

The range of a real function is the set of the real numbers (values) that the function can return (the ouput of the function).

To figure out the range of a function, you first must figure out the domain.

The domain of the function    is all real values, since the cube root function is defined for all the real numbers.

Since this function is continuous (which the translation of the function shows graphically), and the function is defined for all negative and positive values, the range of    is all real numbers.

A vertical translation just slides the function vertically. Since the original function does not have either lower or upper bound, but the limits when x approaches ± ∞ are ± ∞, a translation will not modifiy the range.

Thus, the range of the translated function is (-∞, ∞).

That can also be written as {y|y is a real number}, which is read "y such that y is a real number", and is the last choice of the list.