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.

4xx4x)x(f 23 • Example 1:

Find f(3) for function f, where

Slide 2

Evaluating a Function

• If the value of x is more difficult that a simple integer, the Store function is very useful.

4xx4x)x(f 23 • Example 2:

Evaluate the function where x = 3/4.

(1) Enter 3/4 and press STO

(2) Press x and then press ENTER.

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.

4xx4x)x(f 23 • 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.

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

4xx5

3x

3

2)x(f 23

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.

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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