It is really simple, although maybe not completely intuitive...however the end behavior of any function can be seen as the value that the function would approach as if only the highest powered variable existed...
In this case the end behavior will be that of πx^7 as x→±oo
Since this is an odd power, and has a positive coefficient, π, the end behavior will be:
f(x)→-oo as x→-oo and f(x)→+oo as x→+oo