Question

YOU GET 100 POINTS!!!! Select the correct graph.

Based on the end behaviors, which graph is the graph of f(x) = -2x4 − 4x3 + x2 + x + 3?

Answer 1

Given:

The function is

`f(x)=-2x^4-4x^3+x^2+x+3`

To find:

The graph of the function by using the end behaviors.

Solution:

We have,

`f(x)=-2x^4-4x^3+x^2+x+3`

The degree of the polynomial is 4 which is even and the leading coefficient is -2, which is negative. So,

`f(x)\to -\infty\text{ as }x\to -\infty`

`f(x)\to -\infty\text{ as }x\to \infty`

It means, the graph of the function approaches to negative infinity on the both ends.

Therefore, the correct option is C.