Question

I just need a quick letter answer please and thank you.

Answer 1

Given the function:

`f(x)=-4x^6+6x^2-52`

You can identify that its Leading Coefficient is:

`-4`

And its degree is:

`Degree=6`

Because its highest exponent is 6.

By definition, when the Leading Coefficient is negative and the Degree of the function is Even, its end behavior is:

`f(x)\rightarrow-\infty,\text{ as }x\rightarrow-\infty`
`f(x)\rightarrow-\infty,\text{ as }x\rightarrow+\infty`

Therefore, both ends of the function go in the same direction (to negative infinite).

Hence, the answer is: Option D.