Traditionally, functions are referred to by single letter names, such as f, g, h and so on. Any letter(s), however, may be used to name a function. Examples:
The f (x) notation is another way of representing the y-value in a function, y = f (x). The y-axis may even be labeled as the f (x) axis, when graphing. Ordered pairs may be written as (x, f (x)), instead of (x, y).
Note: The notation f : X → Y tells us that the function"s name is "f " and its ordered pairs are formed by an element x from the set X, and by an element y from the set Y. (The arrow → is read "is mapped to".) it allows for individual function names to avoid confusion as to which function is being examined. Names have different letters, such as f (x) and g (x). The graphing calculator does distinctive function naming with Y1, Y2, ... it quickly identifies the independent variable in a problem. f (x) = x + 2b + c, where the variable is "x". it quickly states which element of the function is to be examined. Find f (2) when f (x) = 3x, is the same as saying, "Find y when x = 2, for y = 3x."
(the bar arrow means the element "x is mapped/matched to 3x + 2")
To evaluate a function, substitute the input (the given number or expression) for the function"s variable (place holder, x). Replace the x with the number or expression. Given the function f (x) = 3x - 5, find f (4). Solution: Substitute 4 into the function in place of x. f (4) = 3(4) - 5 = 7. This answer can be thought of as the ordered pair (4,7). The answer may also be referred to as the image of 4 under f (x). Find the value of h (b) = 3b2 - 2b + 1 when b = -3. Solution: Substitute -3 into the function in place of b. h (-3) = 3(-3)2 - 2(-3) + 1 = 34. Find g (2w) when g (x) = x2 - 2x + 1. Solution: When substituting expressions, like 2w, into a function, using parentheses will help prevent algebraic errors. For this problem, use (2w). g (2w) = (2w)2 - 2(2w) + 1 = 4w2- 4w +1 (Note: the answer is in terms of w.