Answer
Continuous
Work Step by Step
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$
