A catering company specializes in dinners for large groups. They advertise: that “We can seat your entire party at one table; no function is too large for us.” Here’s how they do it.
They have a large supply of folding tables. Each table seats four people. To make a larger table they simply place two tables next to each other, then three in a row, and so forth. All the tables are in one row.
How many people can sit at two tables? Five tables? Ten tables?
Can you find a general rule or formula for the number of people P, who can sit at T tables? Explain how you know your rule is correct.
This is an example of a mathematical function, a rule relating two variables, so that if you know one of the variables, called the independent variable, the rule tells you the value of the other variable, the dependent variable. In this example, T is the independent variable and P is the dependent variable. We say that P is a function of T.
T (tables) |
P (people) |
1 |
4 |
2 |
6 |
3 |
|
4 |
|
5 |
|
… |
|
10 |
|
|
|
T |
|
Hint:
First, it may help you to make drawings of several situations to help understand the rule. You might want to use graph paper.
Second, a very important step in understanding any function is to make a table showing corresponding values of the variables. It’s easier to read if you put the independent variable on the left as we have done here.
After you’ve tried this for yourself check our solution. |
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