How is the graph of (y=-\sqrt{x}) related to (y=\sqrt{x})?

Correct answer: Reflection in the (x)-axis

The direct answer is option A: reflection in the x-axis. Start with a point \((a,b)\) on \(y=\sqrt{x}\), where \(b=\sqrt a\) and \(a\ge0\). In \(y=-\sqrt{x}\), the same x-value gives height \(-b\), so the point becomes \((a,-b)\). This is exactly reflection across the x-axis. Option A is correct. Option B would replace x by \(-x\), producing a y-axis reflection such as \(y=\sqrt{-x}\), not the given function. Option C would require adding 1 outside the function, such as \(y=\sqrt{x}+1\). Option D would require replacing x by \(x-1\), such as \(y=\sqrt{x-1}\). The domain remains \(x\ge0\), while the range changes from \(y\ge0\) to \(y\le0\). Exam cue: a minus outside a function changes y-values; a minus inside the input changes x-direction.