Question

Describe the end behavior of the following function: f(x)=7x^2-3x^2-6

Answer 1

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) --> - ∞