Decide whether the equation describes a function. \( x=y^{2} \)

To determine whether the equation \( x = y^2 \) describes a function, we need to check if for every value of \( x \), there is exactly one corresponding value of \( y \). 1. **Rearranging the equation**: The equation can be rewritten as \( y^2 = x \). 2. **Analyzing the equation**: - For a given value of \( x \), if \( x \) is positive, there are two possible values of \( y \) (one positive and one negative) because both \( y \) and \( -y \) will yield the same \( y^2 \). - If \( x = 0 \), then \( y = 0 \) is the only solution. - If \( x \) is negative, there are no real values of \( y \) that satisfy the equation since the square of a real number cannot be negative. 3. **Conclusion**: Since there are values of \( x \) (specifically positive values) that correspond to two different values of \( y \), the equation \( x = y^2 \) does not satisfy the definition of a function, which requires that each input (value of \( x \)) has exactly one output (value of \( y \)). Thus, the equation \( x = y^2 \) does not describe a function.