Transformed Function The graph of \( f(x)=|x| \) is reflected across the \( x \)-axis and translated right 8 units. Which statement about the transformed function is correct? The domain is the same as the parent function's domain. The graph opens in the same direction as the parent function. The range is the same as the parent function's range. The vertex is the same as the parent function's vertex.

When you reflect \( f(x) = |x| \) across the \( x \)-axis, you get \( f(x) = -|x| \). Translating this function right by 8 units gives you \( f(x) = -|x - 8| \). Now, regarding the statements: the domain remains the same at all real numbers \((-∞, +∞)\) since shifting does not affect it, making that statement correct! However, the graph now opens downward—opposite to the original function, and the range changes as well; it's \( (-∞, 0] \) instead of \([0, +∞)\), so those aspects are incorrect. Lastly, the vertex moves from (0, 0) to (8, 0), thus altering the original position. So, the only true statement is that the domain is the same as the parent function's domain!