Given the function below
[tex]y=\frac{1}{3}x^5-2x^4+\cdots+x-6[/tex]The end behavior of a function describes it behavior as x approaches +∞ and -∞
The leading term of the given function is
[tex]\begin{gathered} \frac{1}{3}x^5 \\ \text{And the degree is 5 which is odd} \\ The\text{ leading coefficient is positive }\frac{1}{3} \end{gathered}[/tex]Where f(x) = y
When x approaches to -∞, f(x) approaches -∞ and when x approaches +∞, f(x) approaches +∞
Hence, the answer is
[tex]\begin{gathered} As\text{ x}\rightarrow-\infty,f(x)\rightarrow-\infty \\ As\text{ x}\rightarrow+\infty,f(x)\rightarrow+\infty \end{gathered}[/tex]