determine whether the equation represents y as a function of x. x^2+y^2=4

Question

anonymous · Answer

No.  This is a relation only.

anonymous · Answer

nope.  this is a circle with center (0,0) radius 2 to fails vertical line test

anonymous · Answer

also notice that (0,2) and (0,-2) fits this equation, so two inputs give different outputs.  says the same thing really

anonymous · Answer

how about x+ y^2=4

anonymous · Answer

No again.  If you were to solve  for y you would get$$y= \pm \sqrt{4-x}$$indicating two y-values for each choice of x

anonymous · Answer

thank you.

anonymous · Answer

(except x=4)

Suppose x=-5, then$$y= \pm \sqrt{4-(-5)}= \pm \sqrt{9} = \pm3$$This implies the points (-5, -3) and (-5, 3).  One domain value is paired with more than one range value.  Therefore not a function in x.