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

Question 642585: Determine whether the equation represents y as a function of x.
x^2+y^2=4
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
A relation is not a function if it assigns more than one y value to any x value in its domain.
For x=0, the equation gives us y=2 and y=-2.
That is enough to say that the equation does not represent y as a function of x.
In fact, the equation represents a circle centered at (0,0) with radius 2.
For any x such that , the equation assigns two values of y.
If you just had the graph corresponding to that equation,

you would know that it is not a function because there is a vertical line x=k that crosses the graph at two points.
(There is really an infinite number of such lines, but one is enough to prove it's not a function).
RELATED QUESTIONS
Determine whether or not the equation represents y as a function of x.... (answered by solver91311)

Determine whether the equation represents y as a function of x... (answered by Alan3354)

Determine whether or not the equation represents y as function of x? Explain your... (answered by josgarithmetic)

Determine whether the equation represents y as a function of x.... (answered by foxxtriton09)

Determine whether or not the equation represents y as a function of x. Please show work. (answered by ikleyn)

determine whether the equation defines y as a function of x.... (answered by josmiceli)

Determine whether the equation defines y as a function of x.... (answered by stanbon,josgarithmetic)

Determine whether the following equation defines y as a function of x... (answered by Fombitz)

Determine whether or not the equation represents y as a function of x. Please show work. (answered by ikleyn)