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How to Compose Functions on the TI-84 Plus

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.

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