## Precalculus (6th Edition) Blitzer

Let $f\left( x \right)={{a}_{n}}{{x}^{n}}+{{a}_{n-1}}{{x}^{n-1}}+\cdot \cdot \cdot +{{a}_{1}}x+{{a}_{0}}$ be a polynomial of degree $n$. The number of negative real zeros of the polynomial function is equal to the number of polynomial function $f\left( -x \right)$ sign changes or less than the number of sign changes. Also, $f\left( -x \right)=f\left( x \right)$ , function is even $f\left( -x \right)=-f\left( x \right)$ , function is odd. Hence, $f\left( -x \right)$ make sense according to the given statement.