Without using technology describe the end behavior of f(x)=3x^32+8x^2-22x+43

The end behavior of any function as x approaches ±oo is equivalent to what the highest power variable would do as x approaches ±oo.

In this case 3x^32 defines what happens.

Since 32 is the power, whether x=±oo, y will approach +oo either way.

So the end behavior of f(x) is to approach +oo at either extreme for x.