The question asks for the value of the variable $a$ such that the function $y(x)$ becomes continuous at the point $x = 0$.

To proceed, we would typically need the definition of the function $y(x)$. Without that, it's difficult to precisely determine the required value of $a$.

Could you provide more information about the function $y(x)$? Is there a function expression provided elsewhere?

If you'd like to explore more:

1. What are the general conditions for continuity of a function at a point?
2. What is the definition of a removable discontinuity?
3. How is a piecewise function made continuous by adjusting parameters?
4. What role does the limit play in determining continuity at $x = 0$?
5. What other points could be interesting to analyze for continuity of a function?

Tip: To ensure a function is continuous at $x = 0$, check that the limit of the function as $x \to 0$ from both sides equals the function value at $x = 0$.