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

 

Functional Notation:

Traditionally, functions are referred to by the letter 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, especially when graphing.  The y-axis may even be labeled as the  f (x) axis.

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")


 

Evaluating Functions:

To evaluate a function, simply replace the function's variable (substitute) 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.   
                            
 


 

Check out how to use your TI-83+/84+ graphing calculator to evaluate expressions and functions. Click here.