Determine whether the following function is continuous at a. Use the continuity checklist to justify your answer.
$$y=\frac{7x-2}{x^2-9x+14},a=2$$
Select all that apply.
A. The function is continuous at $a=2$
B. The function is not continuous at $a=2$ because $f(2)$ is undefined
C. The function is not continuous at $a=2$ because $\underset{x\to 2}{lim}f(x)$ does not exist.
D: The function is not continuous at $a=2$ because $\underset{x\to 2}{lim}f(x)\ne f(2)$.

Step 1 ：To determine whether the function is continuous at a given point, we need to check three conditions: 1. The function is defined at the point. 2. The limit of the function as x approaches the point exists. 3. The limit of the function as x approaches the point is equal to the function's value at that point.

Step 2 ：Let's start by checking the first condition. We need to substitute $x=2$ into the function and see if it's defined.

Step 3 ：The function is not defined at $x=2$ because substituting $x=2$ into the function gives an undefined value. Therefore, the function is not continuous at $x=2$.

Step 4 ：Final Answer: $\boxed{{\displaystyle \text{B. The function is not continuous at }a=2\text{ because }f(2)\text{ is undefined}}}$.