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A function is a rule which maps a number to another unique number. In other words, if we start off with an input, and we apply the function, we get an output. For example, we might have a function that added 3 to any number. So if we apply this function to the number 2, we get the number 5.
A function is a rule which assigns to a real number a new real number. The function f(x) = x3 2x for example assigns to the number x = 2 the value 23 4 = 4. A function is given with a domain A, the points where f is de ned and a codomain. B a set of numbers which f can reach.
The idea of mapping gives us an alternative way to describe a function. We could say that a function is a rule that assigns a unique object in its range to each object in its domain. Take for example, the function that maps each real number to its square. If we name the function f, then f maps 5 to 25, 6 to 36, −7 to 49, and so on.
For each of the examples below, determine whether the mapping makes sense within the context of the given situation, and then state whether or not the mapping represents a function. Express each of the following rules in function notation.
1 Basics. We begin this discussion of functions with the basic de nitions needed to talk about functions. De nition 1. Let X and Y be sets. A function f from X to Y is an object that, for each element x 2 X, assigns an element y 2 Y . We use the notation f : X ! Y to denote a function as described.
function of two variables f(x, y) is a rule which assigns to two numbers x, y a third number f(x, y). For example, the function f(x, y) = x2y+2x assigns to (3, 2) the number 322 + 6 = 24. The domain D of a func-tion is set of points where f is defined, the range is {f(x, y) | (x, y) ∈ D }.
A function is an object f that takes in an input and produces exactly one output. f. (This is not a complete definition – we'll revisit this in a bit.) High School versus CS Functions. In high school, functions usually were given by a rule: f(x) = 4x + 15 In CS, functions are usually given by code: int factorial(int n) { int result = 1;
