Graphs and Functions are very useful in the sciences, financial world, and dealing with statistics. By using graphs you can basically show a relationship between two or more parameters. A function is the mathematical expression that can describe the relationship.
You always see commercials, tv, movies where someone is presenting some graph that is going up or down. Why do they do that? Because in real life, people need to show how a company or their group is doing to other people. The easiest way is to show that on a graph. An example might be how many cars did you sell over a year? You can put a graph up and show how many cars per month you sold and then plot it out. If you have a upward trend you can see that you are doing better each month!
That was just a simple example. Real life models of things are a lot more complicated and the functions, the math involved can be quite complicated. By using graphs and functions, scientists, analysts, politicians, doctors, whatever the field you are in, you can have a simple chart to look at to see trends, tendencies, etc of two or more parameters. If you can find a function that fits the trend you might be able to predict what the future may be like. That is why math, graphs and functions are so important and that is why people who know math, science, statistics, and such skills can find good high paying jobs.
If you think about it you can basically use any two parameters and try to relate them in a graph. Sometimes they are not related and you won't get anything useful! If you know what you are doing you can gain a lot.
Let me give you a more complicated example from my work.
One of my projects is to study the foam from the Columbia shuttle disaster. I run simulation tests to see how the foam coming off the fuel tank damages the shuttle. There are a variety of parameters that affect the foam as it hits the shuttle. Some of these parameters include, location of hit, speed of foam debris, mass of foam, density of foam, what time it hit the shuttle, energy of the debris, volume of the debris and so forth. There are many many many parameters! It would be a pain to look at each number to try to figure it out. I put it all on different types of graphs such as histograms, log/log plots, and so forth. I look for relationship between each parameter and how it affects the hit on the shuttle and the damage the shuttle takes. Without the graph i do not see the "trend line" as well as if i was just looking at numbers. I need a function or an equation to fit the trends. If I know this function then I can explain how each parameter effects the damage to the shuttle and how sensitive it is. That is the ultimate goal. Having done the analysis I can present this to NASA people and then they can say, Ha, the foam is doing this so we shouldn't be doing this anymore or something. The point is, that the graphs and functions are useful to figure out important information that is useful in real life.
There are a myriad of examples you can choose from.