Composite Functions Consider a person working for a concrete contractor. One of his jobs is to estimate the cost for the product to put in a concrete driveway. He would first estimate the surface area of the driveway:

The area is given by:

Assume the thickness of the concrete will be 4 inches. The volume of concrete will be:

Since concrete is sold by the cubic yard, we now convert:

The cubic yards can now be multiplied by the cost for a yard of concrete, and we have the total cost of the product.

Notice the progression in our work. Determine Area: Determine Volume: Determine Volume in Yards:

This is an example of a … COMPOSITE FUNCTION

Step 1: calculate the first function, in this case AREA. length width area Inputs Output

Step 2: calculate the second function, in this case Volume. length width area …becomes the new Input Output Volume (cubic feet) Output

Step 3: calculate the third function, in this case Volume in cubic yards. length width area Output Volume (cubic feet) Output Input Volume (cubic yards)

Notice that in the second and third functions, the INPUT was the previous OUTPUT! This is how one function gets “inside” the other to create a COMPOSITE FUNCTION.