Decide whether the equation describes a function. $$ x=y^{2} $$

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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.
The equation $$ x = y^2 $$ does not describe a function because for some values of $$ x $$, there are two different values of $$ y $$ that satisfy the equation.

Decide whether the equation describes a function.

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