Question

How can we know whether an equation is a function or not?

Answer 1

A function gives you one and only one 'y' value for a specific 'x' value.
f(x)=x+1 is a function.
If we take the equation of a circle
\[x^{2}+y^2=r^2\]
it's not a function because we can have two values 'y' for one 'x'.

P1(x1, y1)
P2(x1, y2)