How do I show that (x+1)^2 + (y-1)^2 = 4 is not a function by giving a value of x to which there corresponds more than one y?
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you need one example ,
where for one x
you have two different y
take x=-1
then
(y-1)^2 = 4
y-1 = (+/-)2
y=3
or
y=-1
(-1,3) (-1,-1)
on a vertical line x=-1
two intersections with graph
so this is not afunction
where for one x
you have two different y
take x=-1
then
(y-1)^2 = 4
y-1 = (+/-)2
y=3
or
y=-1
(-1,3) (-1,-1)
on a vertical line x=-1
two intersections with graph
so this is not afunction
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(x+1)^2 + (y-1)^2 = 4
(y-1)^2 = 4 - (x+1)^2
(y-1)^2 = 4 -x^2 -2x -1
(y-1)^2 = -x^2 -2x + 3
(y-1) = sqrt(-x^2 -2x + 3)
y = 1 +/- sqrt(-x^2 -2x + 3)
since it's plus or minus, there are 2 y's for an x
let x = -2
y = 1 +/- sqrt(-4 + 4 + 3)
y = 1 + sqrt(3) ; 1 = sqrt(3)
(y-1)^2 = 4 - (x+1)^2
(y-1)^2 = 4 -x^2 -2x -1
(y-1)^2 = -x^2 -2x + 3
(y-1) = sqrt(-x^2 -2x + 3)
y = 1 +/- sqrt(-x^2 -2x + 3)
since it's plus or minus, there are 2 y's for an x
let x = -2
y = 1 +/- sqrt(-4 + 4 + 3)
y = 1 + sqrt(3) ; 1 = sqrt(3)
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You have to solve for y using algebra, to show a positive or negative x.