## Precalculus (6th Edition) Blitzer

The statement "I evaluated a polynomial function at 3 and obtained 7, so 7 must be $\underset{x\to 3}{\mathop{\lim }}\,f\left( x \right)$ " makes sense.
If $f$ is a polynomial function, then $\underset{x\to a}{\mathop{\lim }}\,f\left( x \right)=f\left( a \right)$ for any number $a$, which is equal to value of the polynomial evaluated at $a$. As the value of the polynomial function evaluated at 3 is 7 so $\underset{x\to 3}{\mathop{\lim }}\,f\left( x \right)$ is 7. Thus, the given statement makes sense.