Can the variable x be seen as a function of y, like x=g(y)?

[jaybone]

The equation I'm working with is x^2 + (y-2)^2 = 1 and the centerpoint of the circle is R(0,2).

The question I'm having trouble answering is "Can the variable x be seen as a function of y, like x=g(y)?" and "Can the variable y be expressed as a function of x, like y= h(x)?" I believe the answer is no because the there are multiple outputs for the inputs.

for "Can the variable x be seen as a function of y, like x=g(y)?"
I get x alone on one side by subtracting 1 from both sides
x^2+(y-2)^2-1=0
now I subtract x^2 from both sides to get x as a function of y correct?
(y-2)^2-1=-x^2

would x=g(y) look like (y-2)^2 -1=-x^2?

and similarly for y= h(x), would y expressed as a function of x look like x^2-1=-(y-2)^2?

 

[Dr.Peterson]

Neither variable is a function of the other, for the reasons you state. You omitted the final steps of taking the square root, presumably because you already see at that point that there will be two solutions in each case. Asking, "would x = g(y) look like" something that is not solved for x is confusing; the answer is no in any case.

You can also just look at the graph of the circle to see that it fails both the vertical and horizontal line tests.

 

[jaybone]

Thanks!