## Precalculus (6th Edition) Blitzer

The function $f\left( x \right)=c$ is not discontinuous for any number.
Consider the rational function $f\left( x \right)=c$, Here, $p\left( x \right)=c\text{ and }q\left( x \right)=1$ $p\left( x \right)=c$ is a constant function and a constant function is continuous for every number x. Now, find the zeros of the function $q\left( x \right)=1$ by substituting $q\left( x \right)=0$, That is, $1=0$ As $1\ne 0$ so, there is no zero of the function $q\left( x \right)=1$. Thus, the function $f\left( x \right)=c$ is not discontinuous for any number.