Questions: Does the equation (x+4=y^2) define (y) as a function of (x) ?

Solution Steps

To determine whether the equation \( x + 4 = y^2 \) defines \( y \) as a function of \( x \), we need to check if for every value of \( x \), there is exactly one corresponding value of \( y \). In this case, solving for \( y \) gives two possible values (positive and negative square roots), which means \( y \) is not uniquely determined by \( x \).

Given the equation \( x + 4 = y^2 \), we need to determine if \( y \) is a function of \( x \). This means for each \( x \), there should be exactly one \( y \).

Solving the equation for \( y \): \[ y^2 = x + 4 \] \[ y = \pm \sqrt{x + 4} \]

The solutions \( y = \sqrt{x + 4} \) and \( y = -\sqrt{x + 4} \) indicate that for each \( x \), there are two possible values of \( y \). This means \( y \) is not uniquely determined by \( x \).

Final Answer