[tex]\begin{gathered} As\text{ x }\rightarrow-\infty,\text{ f(x) }\rightarrow-\infty \\ As\text{ x }\rightarrow+\infty,\text{ f(x) }\rightarrow-\infty \end{gathered}[/tex]Explanation:[tex]f(x)=-2x^6+4x^4-x^3+8x\text{ - 2}[/tex]
leading coefficient = -2 and it is negative
the highest degree is 6 and it is even
When the leading coefficient is negative and the degree is even:
as x tends to negative infinity, f(x) tends to negative infinity
as x tends to positive infinity, f(x) tends to negative infinity
[tex]\begin{gathered} As\text{ x }\rightarrow-\infty,\text{ f(x) }\rightarrow-\infty \\ As\text{ x }\rightarrow\text{ +}\infty,\text{ f(x) }\rightarrow\text{ -}\infty \end{gathered}[/tex]
