Question

Describe the end behavior of the graph of the polynomial function: f(x) = 2x^(5) - 7x^(2) - 4x

Answer 1

if x is a "big" negative number then x^5 is a "huge" negative number so the graph would be in the 3rd quadrant. Similarly if x is far to the right x^5 is a huge positive number so the graph is in the first quadrant.
So we say that the graph enters in the third and leaves in the first.