Question

The graph shows a vertical translation of y = RootIndex 3 StartRoot x EndRoot.

On a coordinate plane, a cube root function goes through (negative 4, negative 4), has an inflection point at (0, negative 2.5), and goes through (4, negative 1).

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}

Answer 1

y = ∛x has range all real numbers. A vertical translation (here down 2.5) does not change that — outputs can still be arbitrarily large positive or negative.

So the range is {y | y is a real number}.