Graphs are important representations of real-life phenomena (Gelfand, Glagoleva, & Shnol, 1996). They help a mathematician or physicist to visualize and have a clear picture of things. For instance, in a medical research facility, doctors may want to know the effect of a drug on a certain disease. They may collect a lot of data but for them to clearly see the effect of the drug on the disease, they need a visual tool such as a graph.
In my life, there are many variables that can be described by a function which can later be plotted on a graph. For instance, the amount of time I spend on the internet everyday is a function of many things. Let’s use the letter ‘M’ to represent the mean amount of time I spend browsing the web everyday averaged over the entire month. As an example, if M = 2 for the month of January, then it means that, on average, I spent 2 hours browsing the web every day in the month of January.
Among other things, M is a function of months or the time of the year. Mathematically, we can represent this as,
M = f(m)
This is because different times of the year have different weather conditions and different activities. For instance, during winter, it becomes too cold for many outdoor activities. Therefore, I spend more time browsing the year than at any other time of the year. Again, during months such as April and November when the exams are just around the corner, I tend to spend less time browsing and more time reading for exams. M is also a function of other things such as my emotional and physical health. When am depressed, I prefer doing physical activities to sitting on a laptop browsing. However, the graph that will be plotted will only concentrate on M as a function of the time of the year (denoted by ‘m’ – month). The following table shows the average amount of time I spent on the internet in different months of 2010.
The corresponding graph for the data above is shown on the graph below
Figure 1. Graph showing M as a function of m. This figure illustrates the mean amount of time, M, I spend browsing the web everyday averaged over the entire month for all months of 2010. The graph was plotted with the help of Microsoft Office’s Excel.
Gelfand, I. M., Glagoleva, E. G., & Shnol, E. E. (1996). Functions and graphs. Mineola, NY: Dover Publications, Inc.