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

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

Correct!

To determine the end behavior of the graph, we need to analyze what happens to the function as x approaches positive infinity and negative infinity. Specifically, we look at the leading term, which is the term with the highest degree.

In the given function, f(x) = -2x^5 - x^3 + x - 5, the leading term is -2x^5. Since the exponent of x in the leading term is odd, the behavior will be different for positive and negative values of x.

As x approaches positive infinity (x → +∞), the negative sign in front of the leading term doesn't affect the behavior, and the leading term dominates the function. Since -2x^5 approaches negative infinity, the end behavior is downward (or decreasing) to the right.

As x approaches negative infinity (x → -∞), the negative sign in front of the leading term makes the function flip sign. So, -(-2x^5) becomes positive 2x^5. As x approaches negative infinity, 2x^5 approaches negative infinity, meaning the end behavior is downward (or decreasing) to the left.

Therefore, the correct answer is C. Downward to the left and downward to the right.

So based on that the answer would be

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