Question

What is the range of the function `y=2x^3 +5`?

Answer 1

`(-oo, oo)`, all real numbers.

Explanation:

In general, the range of a cubic function `y=a(x+b)^3+c` is all real numbers. Looking at the parent graph `y=x^3,` we see it exists for all values of `y.`

graph{y=x^3 [-10, 10, -5, 5]}

Algebraically, since we have `x^3,` our input for `x` can return positive AND negative values for `y.`