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.