Jazlyn Durham

2022-12-31

How to decide whether the relation $x+y=25$ defines a function?

Expert

It is a FUNCTION if we use the vertical line and the graph of the given relation only intersects at one specific point. 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 $2{x}^{2}-5x=3y$ 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]}

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