How do you test whether a relation is a function (2 Viewers)

[WEMG]

How can you mathematically test whether a relation is a function without vertical line test?

 

[nonsenseTM]

say x^2+y^2=1, y=+/-square root of 1-x^2 , so for every x value , there's more than 1 corresponding y value=>not a function

 

[pman]

vertical line test!!

or prove f(a)=f(b)

 

[nonsenseTM]

vertical line test!!

or prove f(a)=f(b)

y=x^2, but 1^2=(-1)^2=1 i.e. you are saying y=x^2 isn't a function

 

[hscishard]

How can you mathematically test whether a relation is a function without vertical line test?

It's a function if each x value has one y value. You can try subbing one x value into the equation, if it gives only one y value, it's a function.
E.g.
y^2=x let x = 4
y^2=4
y=+/- 2. Two solutions, not a function.

It's best to just draw the equation in your head and use the vertical line test.

This is because y^2=x can have one solution when x=0.