Question

Which piecewise function below represents the function f(x) = x?

A. f(x) = x, for x ≤ 0
B. f(x) = -x, for x < 0
C. f(x) = x, for x > 0

Answer 1

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.