Expert: Bobby Soltani - 9/1/2006

Question
Hi, I am a parent who is trying to help our daughter with a function that contains two rows: The Input row with a set of numbers, and th second row, the Output row with different numbers.  What is this function/equation/type of problem called?  We've heard it refered to as the xy bar or the input output bar.  Can you explain what this is and what is the purpose such as what are we suppose to figure out?  hope you can help.
Thanks,
Gary

Answer
Hi Gary,

I'm not sure exactly what your specific problem is asking, so my answer will be somewhat general.  The xy pairs of numbers simply represent a relationship between two things.  Normally, one of the variables is called the independent variable (e.g. x) and the other is called the dependent variable (e.g. y).  An example may help.

Let's assume that you get paid 3 dollars for every widget you sell.  If you wanted to know how many dollars you made you could write an equation that looks like this:

y = 3x

where x is the number of widgets sold, and y is total number of dollars.  You can see that y is dependent on the input(e.g. number of widgets sold).

Alternatively, you could only have the following information:

When you sold 2 widgets, you received 6 dollars.
When you sold 3 widgets, you received 9 dollars.
When you sold 5 widgets, you received 15 dollars.
When you sold 10 widgets, you received 30 dollars.

Now you have a collection of xy pairs that will allow you to determine the relationship (i.e. function) between the two so you can figure out how many dollars you made for any number of widgets sold.

(2,6)
(3,9)
(5,15)
(10,30)

It is easy to see from this simple example that the relationship is y = 3x.  Often you will need to graph the points to determine the equation that passes through all the points.

I hope this brief explanation helps. Please let me know if you have any other questions.  Good luck.

Bobby