O(n) + O(n) = O(n)?

According to Alex Martelli in O'Reilly's Python in a Nutshell, the complexity class `O(n) + O(n) = O(n)`. So I believe it. But am confused. He explains it by saying that, "the sum of two linear functions of N is also a linear function of N." According to wikipedia, in functional analysis a linear function is a linear map, an example of which would be `f(x+y) = f(x) + f(y)`. Found what seems to be a simpler definition here simply stating, "a linear function is a function who's graph is a straight line." And it includes a few more examples that are less esoteric-looking than the wikipedia article ones. ``` y = f(x) = a + bx ``` and: ``` y = 25 + 5x let x = 1 then y = 25 + 5(1) = 30 let x = 3 then y = 25 + 5(3) = 40 ``` Maybe it would be fair to expect that the sum of two linear equations could be represented on a graph as a straight line which shows something similar to an average between the straight lines that would represent each one. So am I understanding correctly that even though in the following two functions, the "complex" function takes three times as long to process as the "simple" one, they each function in big-O notation as O(n), because the arc of the processing time would be represented by a straight, diagonal line on a plot/graph, and the time difference would be represented by the fact that on a graphic representation, the angle of the more complex function would be sharper? ``` from timer import Timer def complex(it): result = [] for i in it: result.append(i) result.reverse() return result def simple(it): result = list(it) longlist = list(range(0, 1000000)) with Timer() as t: reverse_(longlist) print "=> elapsed time reverse: %s." % t.secs with Timer() as t: straight(longlist) print "=> elapsed time straight: %s" % t.secs ```