f(x+y) = f(x) + f(y) for all real x,y. Setting x = y = 0: f(0) = 0. Setting y = -x: f(-x) = -f(x) (odd function). For rational x, f(x) = f(1)*x. With continuity (or monotonicity), f(x) = kx for all real x. In JEE, the continuity condition is always assumed. If additionally f(1) = c is given, then f(x) = cx.