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

1 Answer
Mar 24, 2018

Answer:

#(-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.#