Final answer:
The piecewise function representing f(x) = x for all real numbers is option A, where f(x) is defined as x for all x less than or equal to zero, without any further restrictions on the domain.
Step-by-step explanation:
The piecewise function that represents the function f(x) = x is option A: f(x) = x, for x ≤ 0. This is because the function f(x) = x is defined for all real numbers, and option A defines f(x) as x without restricting the domain positively or negatively. Option B creates a piecewise function with f(x) = -x for x < 0, which changes the original function for negative values of x. Option C restricts the function to x > 0 and does not represent f(x) = x for values of x that are less than or equal to zero.