Determine whether the relation represents \( y \) as a function of \( x \). \[ x^{2}+y^{2}=36 \] This relation is a function because there are values of \( x \) that correspond to more than one value of \( y \). This relation is a function because there is only one value of \( y \) for each input \( x \). This relation is not a function because there are values of \( x \) that correspond to more than one value of \( y \) This relation is not a function because there is only one value of \( y \) for each input \( x \).

This relation represents a circle with a radius of 6 centered at the origin. When you solve for \( y \), you'll see that for certain values of \( x \), such as \( 0 \) or \( 3 \), there are two possible values of \( y \) (positive and negative). This means that for those \( x \)-values, the same \( x \) input generates multiple \( y \) outputs. To determine if a relation is a function, you can use the vertical line test. If you can draw a vertical line that intersects the graph in more than one point, then it's not a function! In the case of the given equation \( x^{2}+y^{2}=36 \), a vertical line would indeed hit the circle at two points for many values of \( x \), which confirms it is not a function.