Which of the following describes the end behavior of the graph of the function
f(x) = –x6 – 3x4 + 7x – 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
for large ± numbers the first term , -x^6 ,
is the "dominating" term, the other terms become more and more insignifant.
try a large positive + number,
e.g. x = 100
-x^6 = -1000000000000
x = -100
-x^6 = -1000000000000
so what do you think happens at both ends?
something
To determine the end behavior of the graph of the function f(x) = –x^6 – 3x^4 + 7x – 5, we need to examine the highest degree term, which is x^6.
When x approaches negative infinity (or a very large negative number), the sign of the highest degree term will determine the direction of the graph. In this case, since the coefficient of the x^6 term is negative (-1), the graph will be downward to the left.
On the other hand, when x approaches positive infinity (or a very large positive number), the sign of the highest degree term will determine the direction of the graph. In this case, since the coefficient of the x^6 term is still negative (-1), the graph will be downward to the right.
Therefore, the correct answer is:
c. downward to the left and downward to the right