Determine whether the following function is continuous at a. Use the continuity checklist to justify your answer.
\[
y=\frac{7 x-2}{x^{2}-9 x+14}, a=2
\]
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 $\lim _{x \rightarrow 2} f(x)$ does not exist.
D: The function is not continuous at $a=2$ because $\lim _{x \rightarrow 2} f(x) \neq f(2)$.

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: \(\boxed{\text{B. The function is not continuous at } a=2 \text{ because } f(2) \text{ is undefined}}\).