Describe the end behavior of the following function:
F(x) = -x5+ x2 -x
A. The graph of the function starts high and ends high.
B. The graph of the function starts low and ends high.
C. The graph of the function starts high and ends low.
D. The graph of the function starts low and ends low.

Respuesta :

Answer:

C. The graph of the function starts high and ends low

Step-by-step explanation:

For [tex]f(x)=-x^5+x^2-x[/tex], as [tex]x[/tex] approaches negative infinity, [tex]f(x)[/tex] approaches infinity, and as [tex]x[/tex] approaches infinity, [tex]f(x)[/tex] approaches negative infinity.

Thus, we have:

[tex]\lim_{x\rightarrow -\infty}f(x)=\infty,\\\lim_{x\rightarrow \infty}f(x)=-\infty[/tex]

This corresponds with answer choice C. The graph of the function starts high and ends low.