By Jeff McCalla, C. C. Edwards

Sometimes functions are composed together. This may look like, f(g(x)). Function composition is really just substituting one function into another function. Fortunately, you can use your TI-84 Plus calculator to accomplish this task.

Using your graph to compose functions

If you want a graphical representation of function composition, follow these steps:

  1. Enter your functions in the Y= editor.

    Functions are entered in Y1 and Y2 as shown in the first screen.

    image0.jpg

  2. To place your cursor in an open equation in the Y= editor, use the following keys:

    image1.jpg

  3. Press [ALPHA][TRACE] to access the Y-VAR menu and choose the first function you need.

  4. Press [(] and press [ALPHA][TRACE] to access the Y-VAR menu and choose the second function you need.

  5. Press [(], then press

    image2.jpg

    and press [)] twice.

    See the second screen.

  6. Press [GRAPH] to see the graph of the composed function.

    See the third screen.

Using your calculator to compose functions

To evaluate composed functions at a specific x-value, follow these steps:

  1. Enter your functions in the Y= editor.

    Functions are entered in Y1 and Y2 as shown in the first screen.

    image3.jpg

  2. Press [2nd][MODE] to access the Home screen.

  3. Press [ALPHA][TRACE] to access the Y-VAR menu and choose the first function you need.

    See the second screen.

  4. Press [(] and press [ALPHA][TRACE] to access the Y-VAR menu and choose the second function you need.

  5. Press [(], then enter an x-value and press [)] twice.

  6. Press [ENTER] to see the result of your function composition.

    See the third screen.