cide whether the relation defines a function. \( \begin{array}{ll}\text { 8) } y^{2}=x & \text { B) Function }\end{array} \)

To determine whether the relation \( y^2 = x \) defines a function, we need to check if for every value of \( x \), there is exactly one corresponding value of \( y \). 1. **Understanding the relation**: The equation \( y^2 = x \) implies that \( y \) can take on both positive and negative values for a given positive \( x \). Specifically, if we solve for \( y \), we get: \[ y = \sqrt{x} \quad \text{and} \quad y = -\sqrt{x} \] This means that for each positive \( x \), there are two corresponding values of \( y \) (one positive and one negative). 2. **Checking the definition of a function**: A relation is a function if each input (in this case, each \( x \)) has exactly one output (the corresponding \( y \)). Since we found that for each positive \( x \), there are two outputs (both \( \sqrt{x} \) and \( -\sqrt{x} \)), this violates the definition of a function. 3. **Conclusion**: The relation \( y^2 = x \) does not define a function because it does not satisfy the criterion of having a unique output for each input. Thus, the answer is: - **B) Not a function**.