What is the range of the function #x^3 - 5#?

1 Answer
Sep 22, 2017

Answer:

#{y in RR | -oo< y < oo}#

or in interval notation:

#(-oo , oo)#

Explanation:

The function is continuous so is valid for all #x# in #RR#.

So:

as #x -> -oo#

#x^3 - 5-> -oo#

as #x -> oo#

#x^3 - 5-> oo#

So the range is:

#{y in RR | -oo< y < oo}#

or in interval notation:

#(-oo , oo)#

See graph:

graph{x^3 -5 [-10, 10, -20, 20]}