Functional Notation and Evaluating Topic Index | Algebra2/Trig Index | Regents Exam Prep Center

 Functional Notation:

Traditionally, functions are referred to by the letter name  f,  but f need not be the only letter used in function names.  The following are but a few of the notations that may be used to name a function:    f (x),  g(x),  h(a),  A(t),  ...

Note:  The f (x) notation can be thought of as another way of representing the y-value in a function, especially when graphing.  The y-axis is even labeled as the  f (x) axis, when graphing.

Often times, mathematics has a variety of ways to say the same thing.
Examine these notations that are all equivalent:

 (the arrow is read "is mapped to") (the vertical bar is read "such that")
 It should be noted here that since y = x2 + 7 is a function, it can be renamed as  f (x) = x2 + 7.

 Evaluating Functions:

To evaluate a function, simply replace (substitute) the function's variable with the indicated number or expression.

 1 A function is represented by f (x) = 2x + 5.    Find f (3). To find f (3), replace the x-value with 3.     f (3) = 2(3) + 5 = 11.           The answer, 11, is called the image of 3 under  f (x). 2 Replace the v-values with -2. 3 Replace the x-values with 4a.                                                   Notice that the final answer is in terms of a. 4 To find f (3h+2), replace the x-values with 3h + 2.  Using parentheses for this substitution will help prevent algebraic errors.  Use (3h + 2) when substituting.