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.

   

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

   

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

   

   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.

   

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.