Knowledge Base

Solution 34417: Evaluating Composite Functions for a Specific Value of X on the TI-83 Plus and TI-84 Plus Family.

How can I evaluate the composition of two functions given a specific x-value on the TI-83 Plus and TI-84 Plus Family?

In order to evaluate the composition of two functions, given a specific value of x, refer to the following example.

Example - Find the composition of the following two functions when x = .5:
f(x) = x² + 3x - 2
g(x) = 2x + 3

Please Note: Many textbooks indicate function compositions using the notation f(g(x)) or (f ° g)(x).

Solution: Let Y₁ = f(x) and Y₂ = g(x)

• Press [Y=] to go to the Y= Editor screen.
• Input x² + 3x - 2 into the Y₁ slot, then press [ENTER].
• Input 2x + 3 into the Y₂ slot, then press [ENTER].
• Press [VARS], arrow right to Y-VARS, and select 1:Function from the Y-VARS menu.
• Press 1: Y₁ then press [( ].
• Press [VARS], arrow right to Y-VARS, and select 1:Function from the Y-VARS menu.
• Press 2:Y₂ then press [ )] [ENTER].

The Y₃ slot should read Y₃ = Y₁(Y₂).



• Arrow over to the = sign and arrow up 3 times to select the '=' to the right of Y₁, then press [ENTER] to disable the function from being graphed.

Please Note: The black square surrounding the '=' disappears once the function is disabled.

• Arrow down once and press [ENTER] to disable the Y₂ function from being graphed as well.



• Press [GRAPH] to graph the composite function.
• Press [TRACE] then input .5 and press [ENTER].



The coordinates are displayed, even if CoordOff format is selected. The y-value of 26 is the solution to the problem.

Please see the TI-83 Plus and TI-84 Plus Family guidebooks for additional information.