Finding functions (1 Viewer)

[08er]

Given x^2 + y = 0, is y a function of x? Is x a function of y? How do you do this without vertical line test?

 

[Iruka]

We can rearrange the equation to y=-x^2

Then it is clear that this is function of x, not y.

 

[08er]

thanks but how would you do it according to the definition of a function: that one input number is assigned to one output number....

how can u prove the functions?

 

[Drongoski]

Given x^2 + y = 0, is y a function of x? Is x a function of y? How do you do this without vertical line test?

So y = - x^2 ( upside down parabola of y = x^2)

so x^2 = - y

Therefore x = +/- sqrt(-y) = 2 distinct value except for y = 0

i.e. for every nonzero y, x has 2 distinct values.

That means x is not a function of y, since to be a function of y, every value of y

must lead to one and only one value of x.

 

[08er]

but wouldnt square rooting x^2 give us +/- x, and not just x?