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
I say the answer is C but am not sure. Can someone please explain?
See:
http://www.jiskha.com/display.cgi?id=1248120871
To determine the end behavior of a polynomial function, we examine the leading term of the function.
In this case, the leading term of the function is -2x^5. Since the degree of the polynomial is odd and the leading coefficient is negative (-2), we can conclude that:
- As x approaches negative infinity, the function will go downward (fall) to the left.
- As x approaches positive infinity, the function will go downward (fall) to the right.
Therefore, the correct answer is C. Downward to the left and downward to the right.