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 the graph of a function, we examine the leading term of the polynomial.
In this case, the leading term is -2x^5.
Remember that the degree of a polynomial is determined by the highest power of x in the function. In this case, the degree is 5.
When the degree of a polynomial is odd, like it is in this case, the end behavior of the graph will mimic the behavior of the leading term.
Since the coefficient of the leading term is negative (-2), the graph will be pointing downwards as x approaches positive infinity. Similarly, as x approaches negative infinity, the graph will also be pointing downwards.
Therefore, the end behavior of the graph is downward to the left and downward to the right.
Hence, the correct answer is option C.
To determine the end behavior of a function, we need to analyze what happens to the graph as x approaches positive infinity and negative infinity.
In the given function, f(x) = -2x^5 - x^3 + x - 5, the highest-power term is -2x^5. Since the degree of the highest power term is odd (5), the end behavior will depend on the leading coefficient (-2).
If the leading coefficient is positive, the end behavior of the graph will be upward to the left and upward to the right. Conversely, if the leading coefficient is negative, the end behavior will be downward to the left and downward to the right.
In this case, the leading coefficient is -2, which is negative. Therefore, the end behavior of the graph of f(x) = -2x^5 - x^3 + x - 5 is downward to the left and downward to the right.
Therefore, the correct answer is C.