Question

The function y = RootIndex 3 StartRoot x EndRoot – 3 is graphed only over the domain of {x | –8 < x < 8}. What is the range of the graph?

{y | –5 < y < 5}
{y | –5 < y < –1}
{y | 1 < y < 5}
{y | 1 < y < –1}

Answer 1

y = ∛x − 3. For -8 < x < 8, ∛x ranges over (-2, 2). Subtracting 3 gives y ∈ (-2−3, 2−3) = (-5, -1).

Answer: {y | −5 < y < −1}