What is It
Functions as Mathematical Model
A function relates each element in the domain to only one value in the
range. It indicates a relationship between two quantities by some rule.
Modeling means constructing a set of mathematical equations that describes
a situation, solving the equations, and using them to understand the real-life
problem. Mathematical modeling is a process by which we start with real-life
problems and apply a quantitative solution using the tools of mathematics.
Functions as mathematical models can be written in the form y = f(x).
For whatever acceptable value(s) of the independent variable x, a
corresponding value of y is derived. It can also be used to predict what a
system will do for different values of the independent variable. To construct
an appropriate functional model will lead to a better understanding of various
phenomena.
Example 1: A function C represents the cost of buying x value meals, if one
value meal
costs P45.
Answer: C(x) = 45x.
Example 2: Construct a mathematical model that describes the trend in the
relationship of x and f(x).
x
1
2
3
4
5
f(x)
-4
1
4
11
20
Answer: The pattern shows the relationship for every value of x.
Relationship
x
1
f(x)
-4
2
1
3
4
4
11
5
20
-4=12-5
-1-22-5
4-32-5
11-42-5
20-52-5
Hence, the mathematical model is flx) = x²-5.
​