We can view mathematical functions in three ways: analytical, numerical, and graphical.
To illustrate the differences, let's see how we can express the relationship between the radius \(r\) and area of a circle \(A\) using these approaches:
Analytical
The first viewpoint is analytical. It is when we approach the situation using its mathematical symbols and operations. If we want to look at \(r\)-\(A\) relationship analytically, it is the function by itself: \(A(r)=\pi{r^2}\).
Numerical
The next one is the numerical viewpoint. In this perspective, we create what we call the table of values. It's a table format of inputs and outputs. To construct one:
- First, give multiple inputs for the function and place it in one column. In our example, it would be a list of radius (1, 2, 3, etc.)
- Next, solve for its corresponding output in an adjacent column (\(\pi\), \(4\pi\), \(9\pi\), etc.)
- The resulting table is the table of values.
