ANSWER:
1st option: f(x) = -f(-x)
STEP-BY-STEP EXPLANATION:
The polynomial function is symmetric about the origin in the odds functions, where the following is true:
[tex]\begin{gathered} f(-x)=-f(x) \\ \\ \text{ Therefore:} \\ \\ f(x)=-f(-x) \end{gathered}[/tex]Then it would be:
If f(x) = -f(-x), then the graph of the polynomial function is symmetric about the origin.
The correct answer is the 1st option: f(x) = -f(-x)
