Can a constant function be called a function in $x$?

Question

Suppose I have $y=c$, where $c$ is a constant. We can graph it on the coordinate axes too. Now, which statement is correct to say,

1. $y$ is a constant function of $x$.
2. $y$ is not a function of $x$.

I think that the first statement is correct as if 2nd were correct then vertical line test would have failed. But, I want to confirm if I am thinking correctly or not.

Answer 1

Calling $f(x)=c$ a “constant function of $x$” is not only unuseful, it is also ambiguous:

$y=c$ and $y=c+0x$ both pass through $(0,c),$

whereas $y=cx^0$ has a hole at $0.$