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 | y is a real number}
A or B

Answer 1

B.

Reason: the cube-root function (and any horizontal shift/reflection of it) has range all real numbers. For y = -∛(x+1), for any real y you can solve x = -y^3 - 1, so every real y occurs.