Which statements are true about the function f(x) = –|x| – 2? Check all that apply.

The parent function y = |x| and f(x) = –|x| – 2 are both defined for every real x, so they have the same domain; statement C is true. The negative sign reflects the graph downward, and subtracting 2 shifts it down, making its highest value –2 at x = 0. Thus its range is all real numbers less than or equal to –2, so D is true. The functions open in opposite directions and do not have the same range.

AI-written and checked against the verified answer.