why are the zeros of cubic functions visible on graphs but not on the data points? How do the differences between real data and the graph of an equation contribute to that?
Well I am working on a math problem and it deals with making a cubic graph from the data that was provided and the question asked me where the zeros were on the graph [and I said (0,0)] and the question then states: "Notice that you are able to see the zeros in the graph of the function but not in the graph of your actual data points. What is the reason for that? Think about the differences between real data and the graph of an equation."
I'm not really sure how to answer this and I've tried to look up more details on this online with not much of a success. If it helps the data was height and volume of different figures and I had to graph it. Here are some links of the graph and data tables I made from the assignment.
http://i43.tinypic.com/2ir3v5j.png] < Graph
http://i44.tinypic.com/2zyy910.png < Data
Think about what a zero would mean in the context of the problem you've stated: where volume is a function of height. A zero would mean that the object has no volume at all (even though it has a height)!! Interpreted the other way - where height is a funciton of volume - a zero would imply the object has no height at all (even though it has a volume).
This problem illustrates the difference between what is going on in the real world and the equations that model it (note that they are NOT what is really happening, they are a model of what is really happening). Here the domain of the function (the graph) is limited by reality, not by the math behind the equation.