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

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Answer 1 · 2017-09-22T23:59:27

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

or in interval notation:

#(-oo , oo)#

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]}