Resolved: "How to decide whether the relation x+y=25 defines..."

High School
Algebra
Pre-Algebra
Equations, expressions, and inequalitie

Jazlyn Durham

Answered question

2022-12-31

How to decide whether the relation

x + y = 25

defines a function?

Answer & Explanation

madwindnhe

Beginner2023-01-01Added 7 answers

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} - 4 y = 2 x

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} - 5 x = 3 y

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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