For which x-values do the graphs of f(x)=x^2 and g(x)=|x| meet?

Correct answer: x=0, x=1, and x=-1

The governing concept is the condition for intersection: at a common point, the two functions must have equal y-values for the same x. Hence solve x^2=|x|. Since x^2=|x|^2 for every real x, this becomes |x|^2=|x|, or |x|(|x|−1)=0. Thus |x|=0 or |x|=1. The first condition gives x=0; the second gives x=1 and x=−1. Therefore the complete set is x=−1, 0, and 1, so option A is correct. Option B omits x=±1, and option C omits x=0 and x=−1. For x=±2, x^2=4 while |x|=2, so option D does not represent intersections.