The function f() is a rule that, given a number x assigns a number y. We don’t know what it’s graph would look like for numbers that are less than approximately x = -0.25 and numbers that are greater than approximately x = 4.25. But from the graph we see that f(0) = 1, that f(1) = 2, and that f(2) = 0. The graph also strongly suggests that we are to assume that the function f is continuous, so that we are to assume that lim of f(2x) as 2x approaches 2 is equal to f(2). That is lim of f(2x) as x approaches 1 is 0.
I don’t have the book, so I don’t know what has been said about notions such as the definition of the limit of a function or the definition of continuity. The notion of continuity requires that of a limit.
Please feel free to ask about anything I’ve said that might not seem clear.