Question

If _____________, then the graph of the polynomial function is symmetric about the origin.f(x) = -f(-x)f(x) = -f(x)f(x) = f(-x)f(x) = f(x + 1)

Answer 1

1st option: f(x) = -f(-x)

Explanation:

The polynomial function is symmetric about the origin in the odds functions, where the following is true:

`\begin{gathered} f(-x)=-f(x) \\ \\ \text{ Therefore:} \\ \\ f(x)=-f(-x) \end{gathered}`

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)