We are given a function f(x) = 8x^3 - 7x^2 - 3x + 7. We have to find the range of values between which the values of the function lie.
Now we can see that this is a third degree function and the values of the function are defined for all values of x ranging from -inf. to + inf.
As the values of x change the value of the function also changes and there is no maximum value or minimum value, higher than which or lower than which resp. the value of the function cannot go. Therefore f(x) can take values ranging from -inf. to +inf.
Therefore f(x) = 8x^3 - 7x^2 - 3x + 7 can lie at any value between -infinite and +infinite.
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).