## Precalculus (6th Edition) Blitzer

Recall that if $f$ is a polynomial function, then we have $\lim_\limits{x\to a}f(x)=f(a)$. $f(x)=3x^2-2x+1$ Set $a=4$ $f(4)=3(4)^2-2(4)+1=41$ So, $f(4)$ is defined. Now, $\lim_\limits{x\to 4} f(x)=3\lim_\limits{x\to 4} x^2-2 \lim_\limits{x\to 4} x+1=3(4)^2-2(4)+1=41$ So, $f(x)$ exists. Therefore, the function is continuous at $x=4$