Questions: For the following exercise, determine whether the relation represents Y as a function of X 25. y^2 = x^2

Solution Steps

To determine if the relation \( y^2 = x^2 \) represents \( y \) as a function of \( x \), we need to check if for every value of \( x \), there is exactly one corresponding value of \( y \). A relation is a function if each input \( x \) has exactly one output \( y \).

1. Solve the equation \( y^2 = x^2 \) for \( y \).
2. Check if the solution provides a unique value of \( y \) for each \( x \).

The given relation is \( y^2 = x^2 \). To determine if this represents \( y \) as a function of \( x \), we solve for \( y \). Solving the equation \( y^2 = x^2 \) gives us two solutions: \( y = x \) and \( y = -x \).

For a relation to be a function, each input \( x \) must correspond to exactly one output \( y \). In this case, for any given \( x \), there are two possible values for \( y \): \( y = x \) and \( y = -x \). This means that the relation does not provide a unique value of \( y \) for each \( x \).

Final Answer