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

Question

Ethan Adkins · Accepted Answer

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.

It is a FUNCTION if the vertical line is used and the given relation's graph has only one unique point intersection; 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 apply the vertical line test in testing For instance, the graph}(y^2-4y-2x)(y+10000x-15*10000)=0[-20,20,-10,10]} is NOT A FUNCTION because employing a vertical line will intersect in multiple points. Example: the graph of #2x^2-5x=3y# is a FUNCTION because, using a vertical line will intersect in only one point. graph{y+10000x-2*10000)=0[-20,20,-10,10]} May God bless you all. I hope this explanation helps.

Ethan Adkins · Answer

undefined To decide whether the relation $x + y = 25$ defines a function, we need to check if for every value of $x$, there is exactly one corresponding value of $y$.

In this case, if we solve the equation $x + y = 25$ for $y$, we get:

$$y = 25 - x$$

Since for every value of $x$ there is exactly one corresponding value of $y$, the relation $x + y = 25$ does define a function. This is because each input value of $x$ will yield a unique output value of $y$.