Question

On the coordinate grid, the graph of y = RootIndex 3 StartRoot negative x minus 1 EndRoot is shown. It is a reflection and translation of y = RootIndex 3 StartRoot x EndRoot.

On a coordinate plane, a cube root function goes through (negative 2, 1), has an inflection point at (negative 1, 0), and goes through (7, negative 2).

What is the range of the graphed function?

{x |-2 < x < 2}
{y |-2 < y < 2}
{x | x is a real number}
{y | y is a real number}

Answer 1

{y | y is a real number}

A cube-root function (and any translation/reflection of it) is defined for all real x and takes all real y-values, so its range is all real numbers.