Question

Which statement best describes the end behavior of the following function?

F(x) = 2x4 – x3 +5x-9
A. The graph of the function starts low and gends high.
B. The graph of the function starts high and ends high.
C. The graph of the function starts low and ends low.
D. The graph of the function starts high and ends low.

Answer 1

B. The graph of the function starts high and ends high.

Explanation:

Firstly, we need to determine the degree of the function F(x) = 2x⁴– x³ +5x-9

To find the degree of the function, we add the exponent of each variable, and the variable with the highest exponent is the degree of the exponent.

2x⁴ has degree of 4

– x³ has degree of 3

+5x has degree of 1

-9 has degree of 0

Therefore the degree of the function is 4. Since it is even, the graph would start and end in the same direction.

The coefficient of the highest degree is 2 (2x⁴) which is positive therefore The graph of the function starts high and ends high