Answer:
The function that could possibly have created this graph is:
[tex]F(x)=\dfrac{-1}{3}x^4+7x^2+15x[/tex]
Step-by-step explanation:
As we know that any odd degree polynomial has odd number of real zeros since the complex zero always exist in pair.
Here in the graph we see that there are 4 real zeros.
Hence, the polynomial can't be a odd degree polynomial.
Hence, option: B and Option: C are discarded.
So, we are left with choice A and D i.e. a even polynomial.
Also as we could see that the end behavior of the graph satisfy:
as x→ -∞ F(x) → -∞
Also when x → ∞ then F(x) → -∞
Hence, the even degree polynomial must have a negative leading coefficient.
Hence, option: D is also discarded.
Hence, option: A is the answer.
