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 \( x \).

1. The equation given is \[ x^2 + y^2 = 36. \] 2. This equation represents a circle with center at \((0, 0)\) and radius \(6\). 3. For a relation to be a function, each value of \( x \) must correspond to exactly one value of \( y \). 4. However, in the case of this circle, many values of \( x \) (specifically, for \( -6 < x < 6 \)) yield two values of \( y \) (one positive and one negative). For example, if \( x = 0 \): \[ 0^2 + y^2 = 36 \quad \text{implies} \quad y^2 = 36 \quad \text{or} \quad y = 6 \text{ and } y = -6. \] 5. Since there are values of \( x \) that correspond to more than one value of \( y \), the relation does not represent \( y \) as a function of \( x \). 6. Therefore, the correct statement is: \[ \text{This relation is not a function because there are values of } x \text{ that correspond to more than one value of } y. \]