In the Philippines, jeepneys are the kings of the road. They are our major way of public transport and, of course, the cheapest. As of this writing, the jeepney fare in the Philippines is about 8.00 pesos (about US$0.19) for the first four kilometers and an additional 1.25 pesos (about US$ 0.03) for each succeeding kilometer.
http://rjose.com/Fly2Philippines/Images/Jeepney.jpg
If we are going to create the jeepney fare matrix, where d is the distance traveled in kilometers and F be the fare, then we have the following table for the first 10 kilometers.
It is clear from the table that for each distance traveled, there is a corresponding fare; therefore, fare is a function of distance. The graph of the values in the table above is shown below. For distance greater than 0 up to 4 kilometers, the fare is 8.00 pesos. Since there is no corresponding fare for d=0, we represent the (0,F(0)), and the leftmost part of each horizontal segment with an empty circle. On the other hand, a point exists for (4,F(4)) in the lowest part of the graph so we represent it with a filled circle. F(4) is undefined in the next graph, so again, it is represented with an empty circle. Notice that this is similar to other parts of the graph: the left most part of each graph is undefined.
The function above is a step function because the value of the dependent variable F jumps or steps from one value to another. Step functions are a special type of piecewise function.
*1 dollar equals 43 pesos as of this writing.
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