Final answer:
Functions are multiplied to model complex relationships, not to find the average. The resulting functions are widely used in engineering for optimization and in other fields where complex systems need mathematical analysis. This multiplication of functions is a key tool in understanding real-world scenarios mathematically.
Step-by-step explanation:
A function in mathematics is a rule or a relationship that connects an input to a precisely one output. In the context of real-world applications, we multiply functions to model more complex relationships between various related quantities. For example, in economic models, algebraic functions are commonly used to represent the relationships between different economic factors.
Function multiplication is not meant to find the average, which answers the student's question. Instead, the multiplication of functions serves to model scenarios where one quantity varies as a product of other quantities. For instance, the volume of a rectangular box can be modeled as a function representing the product of its length, width, and height, which are each functions of different variables in more complex scenarios.
In real-life applications, the resulting functions from multiplication are heavily used in fields such as engineering for purposes of optimization. An engineer might multiply functions to optimize material use, cost, and structural integrity in a design. These mathematical models play a crucial role in engineering, but the application of resulting functions is not limited to engineering. They are also found in fields like physics, economics, and biology, wherever complex systems are analyzed mathematically. However, they are not commonly used in literature analysis, which is more qualitative in nature.