# Is the equation x^2+y^2=4 a function?

No - there is more than one $y$ value for each $x$ value in the domain.

#### Explanation:

Equations in the form of $a {x}^{2} + b {y}^{2} = {r}^{2}$ form circles.

${x}^{2} + {y}^{2} = 4 = {2}^{2}$ looks like this:

graph{x^2+y^2-4=0 [-7.023, 7.024, -3.51, 3.513]}

Is this a function? That is, does there exist a single $y$ value for each $x$ value in the domain? And the answer is no - for essentially all the $x$ values (excepting $x = \pm 2$), there are two $y$ values for each $x$ value.

This is often called the "vertical line test" - if you draw a vertical line for any value of $x$ in the domain, does the vertical line encounter no more than one $y$ value. We can see that if we do that (such as draw a line along the $y$ axis), we'll hit two $y$ values.