2C-2. Function Composition
Instructions:
- Use the input boxes for and to define the "inside" and "outside" function for the function composition.
- Use the input box / slider tool for to adjust the input for the inside function. Observe that the output of the inside function becomes the input of the outside function.
- Use the "Trace f(g(x))" button to trace out the graph of the composite function . Use the "Clear" button to erase the trace and turn it off.
- If you need to zoom out or scroll and adjust the domain of the inside function, you can click and drag the points labeled and .
Function Composition
If we think of a function as taking an input of and producing an out of , then we can follow up one function with another function, creating a chain of functions, where the output of one function is used as the input of the next function. (It's like when you do a calculation on your calculator and use a previously stored value to do a new calculation.) Here is a chain:
In this example is the input to the function , which results in an output . Then, is used as the input of f to obtain as the output of the composite function. Notice the order matters:
In this chain, is the input of , which produces the output . Then, is the input of the function , which produces the output .