To analyze the end behavior of this function we just need to evaluate its limit as it goes to infinity and minus infinity.
[tex]f(x)=4x^7+4x^6+2x^2-5[/tex]
The limits of this functions are
[tex]\begin{gathered} \lim _{x\to\infty}f(x)=\infty \\ \lim _{x\to-\infty}f(x)=-\infty \end{gathered}[/tex]
This function goes down as x approaches minus infinity and goes up as x approaches infinity.
