1. Evaluating a Function Given a function y = f(x), we are often interested in finding function values for a given x. One example would be to find ordered pairs for points on the graph of the function. To find just one function value, the simplest way is to substitute 3 for x in the Home Screen. Example 1: Find f(3) for function f, where

2. Slide 2 Evaluating a Function If the value of x is more difficult that a simple integer, the Store function is very useful. Example 2: Evaluate the function where x = 3/4. (1) Enter 3/4 and press STO (2) Press x and then press ENTER.

3. Slide 3 Evaluating a Function The value of.75 or 3/4 is now stored in the variable x. Now repeat the steps of example 1, using x in place of the value. If a fractional form is desired, press MATH and ENTER to select fraction, or Frac. The press ENTER again. The fractional form can be completed in one step.

4. Slide 4 Evaluating a Function Enter function f into Y1. A third way to evaluate a function is given in the next example. Example 3: Find f(7) for function f, where

5. Slide 5 Evaluating a Function Use QUIT to get to the home screen. Then press VARS to get Variables. Use the right arrow to highlight Y-VARS at the top of the screen, and press ENTER. Press ENTER again to paste Y1 into the Home Screen. Now type “(7)” and press ENTER. The result is f(7), the original problem to be solved.

6. Slide 6 Evaluating a Function The evaluation is in approximate decimal form. To find the exact value, use MATH|Frac. Two other ways to evaluate a function are TABLE and TRACE, which are described in other modules. They will always give the function value in terms of a decimal, which may be rounded. Thus, one of the most valuable aspects of Y1( ) is the ability to find exact function values (when x is rational).

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