Question

I don't know if I got the correct answer for the behavior goes to the positive or negative?

Answer 1

Given the function:

$f(x)=-x^5$

by looking at the exponent of x, we can see that it is an odd exponent, then, the graph must look something like this:

but since we have a negative sign (-x^5) ,then, it looks like this:

now we can see that the following limits are true:

$\begin{gathered} \lim _{x\rightarrow\infty}f(x)=-\infty \\ \lim _{x\rightarrow-\infty}f(x)=\infty \end{gathered}$