We are given function : f(x)=7x^3-3x^2-6.
We need to describe the end behavior of the given function.
In order to describe end behavior of a function we need to find the degee and leading coefficient of the given function.
Degree of the given function is the maximum power of the exponent.
We have x^3, there.
Therefore, degree of the given function is : 3 an odd degree and
Leading coefficient is : 7 a positive number.
According to end behavior rule, when degree is an odd degree and leading coefficient is a positive number the f(x) would be of same sign as x.
Therefore end behavior would be
x --> + ∞ , f(x) --> + ∞
x --> - ∞ , f(x) --> - ∞