Answer
The statement “A polynomial function is continuous at every number” is true.
Work Step by Step
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.
