## Precalculus (6th Edition) Blitzer

Consider the polynomial function $f\left( x \right)$, A rational function $f\left( x \right)=\frac{p\left( x \right)}{q\left( x \right)}$ is discontinuous for the points for which the function is not defined, that is, for the zeros of the function $q\left( x \right)$. Thus, for the polynomial function, $q\left( x \right)=1$. Find the zeros of the function $q\left( x \right)=1$ by $q\left( x \right)=0$, $1=0$ As $1\ne 0$, There is no zero of the function $q\left( x \right)=1$. Thus, the function $f\left( x \right)$ is not discontinuous for any number. Therefore, the polynomial function $f\left( x \right)$ is continuous at every number. Hence, the statement is true.