Question

How do you decide whether the relation `x + y = 25` defines a function?

Answer 1

For the relation `x+y=25`, one simple solution to decide if it is a function or not is by graphical solution using "vertical line test". It is a actually a FUNCTION.

Explanation:

If we use the vertical line and there is only one unique point intersection with the graph of the given relation then it is a FUNCTION. Otherwise, it is not.

Kindly see the graph of `x+y=25`
graph{(x+y-25)(y+10000x-15*10000)=0[-50,50,-25,25]}

How to test using the vertical line test

Example: the graph of `y^2-4y=2x` is NOT A FUNCTION because, using a vertical line will intersect in more than one point.
graph{(y^2-4y-2x)(y+10000x-15*10000)=0[-20,20,-10,10]}

Example: the graph of `2x^2-5x=3y` is a FUNCTION because, using a vertical line will intersect in only one point.

graph{(2x^2-5x-3y)(y+10000x-2*10000)=0[-20,20,-10,10]}

God bless....I hope the explanation is useful.