Understanding Functions: Evaluating f(x,y) for Real Numbers | Explained

[mathstudent88]

Let f be the set of all ordered pairs (x,y) such that x and y belong to R and y = x². Is this a function?
The same question, for f be the set of all ordered pairs (x,y) such that x and y belong to R and x=y². Is this a Function?


I think for the first one y=x² it is a function because there is a unique y value for every x value that is given.

For the second one, I think that x=y² is not a function because there is not a unique y value for every x. Because if x=2 then y can = -2 and 2.

Is this right?

Thanks for the help!

 

[edziura]

You are correct.

Also, the graph of y = x^{2} passes the vertical line test.

The 2nd function's graph doesn't.

 

[mathstudent88]

thank you!