What is the range between which the values of the function f(x) = 8x^3 - 7x^2 - 3x + 7 lie?

To find the range of  f(x) = 8x^3 - 7x^2 - 3x +
7.

The range of the function is the set of all real values
of the function for the  set of vaues of the domain of the
function.

The domain of the function is  x taking all the
real values .   Therefore x is in the interval (-infinity ,
infinity.)

Since the highest degree is 3, f(x)  = x^3
(8-7/x-3/x^2+7/x^3)  behaves like x^3 *(a positive
quantiy).

Therefore  f(x) = infinity  as x -->
infinity and

f(x) = -infinity as x-->
-infinity.

Therefore the range of f(x) is  (-infinity ,
infinity).