The range of f(x) =xsgnx is A)all real numbers B)(-infinity,0) C)(-infinity,0] D)[0, infinity)?

The range of a function is the set of all possible output values.

For the function f(x) = xsgnx, the output values are determined by the sign of x.

If x is positive, then f(x) = x.
If x is negative, then f(x) = -x.

Therefore, the range of f(x) is all real numbers, since for any real number x, f(x) can be positive or negative.

So, the correct answer is A) all real numbers.