<s>[INST] Here is the specification (kindly provided by the great Squidwordrex).

**Problem 1.3.5:** Let \( X \) be a set containing only \( 0 \) and \( 1 \), and let \( Y \) be any set and \( Z \) be any set of real numbers. Let \( f: Y \to Z \) be a function. Let \( g: X \to \mathbb{R} \) be defined by 
\[ 
g(x) = \begin{cases} 
f(y) &\mbox{if } x = 0 \mbox{ and } y \in Y, \\
0 &\mbox{if } x = 1, \end{cases} 
\] 
where \( g(0) = f(y) \) is taking an arbitrary value of \( y \in Y \).

So, what is the vertical asymptote of the product of \( f(y) \) and \( g(x) \), if the domain of \( f(y) \) is \( y = 1 \)?[/INST]