Functional Notation and Evaluating
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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.   
                            
 


 

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