I am reading a book about Calculus and in the first chapter it's said there's a test to validate whether a graph is a graph of a function or not. If it's possible to draw a vertical line that touches two points of the graph the graph is not the graph of a function. In other words, no two inputs can map to the same output.
$f(x)=4x$ is a function
$y^2=4ax$ is not
However, to me that doesn't seem to make much sense as we could simply define a bivariate function like $f(x, y)$ as having two inputs instead.
Is there an intuitive way to understand this?