What is function ?

A function is a relation for which each value from the set associated with only one value to another set.

So, only one-to-one relation is consider as a function

One-to-many relation is not a function

Many-to-one relation is not a function

Many-to-many relation is not  a function

Not all relation is a function

Not all equation is a function

all function is a relation

and function is not same as equation

function ≠ equation, but function and equation is relation

Examples

Graph y = 3x + 5




Using 'Vertical Line Test', we can see that for any value of 'x', there is only 1 value for 'y'


Graph \[{{x}^{^{2}}}+{{y}^{2}}-4x-3y-6=0\]


Using 'Vertical Line Test', we can see that for any value of 'x', there are 2 values for 'y'. So, circle graph equation is not a function.