Given:
The function is
[tex]f(x)=-2x^4-4x^3+x^2+x+3[/tex]
To find:
The graph of the function by using the end behaviors.
Solution:
We have,
[tex]f(x)=-2x^4-4x^3+x^2+x+3[/tex]
The degree of the polynomial is 4 which is even and the leading coefficient is -2, which is negative. So,
[tex]f(x)\to -\infty\text{ as }x\to -\infty[/tex]
[tex]f(x)\to -\infty\text{ as }x\to \infty[/tex]
It means, the graph of the function approaches to negative infinity on the both ends.
Therefore, the correct option is C.
