Question

Which of the following describes the end behavior of the graph of the function

f(x) = –2x^5 – x^3 + x – 5?

A. Downward to the left and upward to the right

B. Upward to the left and downward to the right

C. Downward to the left and downward to the right

D. Upward to the left and upward to the right

Answer 1

The dominant term in this polynomial is the highest power, -2x⁵.
The odd numbered powers with a positive coefficient have a shape that goes from bottom left to the top right. Compare that to a straight line with a positive slope.
With a negative coefficient, the graph is mirror about the x-axis. If we base the answer on the dominant term, it would be from top-left to bottom-right.
See following plot of the function for confirmation:
http://i263.photobucket.com/albums/ii157/mathmate/x5.png

Answer 2

So based on that the answer would be

B. Upward to the left and downward to the right ??

Answer 3

Correct!