Which function is obtained when the graph of (f(x)=|x|) is reflected in the (x)-axis?

Correct answer: (y=-|x|)

The direct answer is A: y=-|x|. Reflection in the x-axis sends every point (x,y) to (x,-y). Thus the x-coordinate stays the same, while the sign of the y-coordinate changes. The original graph is y=|x|, a V-shaped graph above or on the x-axis. After reflection, it becomes y=-|x|, a downward V whose values are non-positive. Option A is correct because replacing y by -y changes |x| into -|x|. Option B, y=|x|+1, moves the graph upward by 1; it is a vertical translation, not a reflection. Option C, y=|x-1|, moves the graph one unit right; it is a horizontal translation. Option D, y=x^2, is a different parabola and has no direct reflection relationship here. For a graph y=f(x), reflection in the x-axis is y=-f(x); reflection in the y-axis would instead be y=f(-x). Memory cue: x-axis reflection changes the output sign, while y-axis reflection changes the input sign.