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

$\left(- \infty , \infty\right)$, all real numbers.
In general, the range of a cubic function $y = a {\left(x + b\right)}^{3} + c$ is all real numbers. Looking at the parent graph $y = {x}^{3} ,$ we see it exists for all values of $y .$
Algebraically, since we have ${x}^{3} ,$ our input for $x$ can return positive AND negative values for $y .$