Laura Dickerson

The following is an example of how students might explore the function which "squares x".

First the students, will label which column will be x and which will be y. I suggest that x be first since y is a function of x.

After entering the data, the students can make a graph of their function.

Now students can see that the graph of f(x) is half of a parabola. What if the students want to know what happens if the x values are negative? They can change what values x holds and once again draw the graph.

A teachable moment has just come up. The students should be asked what are similar about the two graphs. The students should also make a conjecture about what if the two graphs were put together, what would this be a graph of? The students should then begin to understand what domain is and what the difference in the domain of the two graphs is. Then the students can verify there conjectures and graph f(x) for all values of x used in the first two graphs.

One may ask, can't this all be done on a graphing calculator? The answer is yes and I suggest that if computers are not available, use graphing calculators. If graphing calculators are not available, pencil and paper is also a great tool. I understand that not all math classrooms have computers available at all times. I visualize though that students learn to use spreadsheets as a mean to solve problems and present solutions. One example finding the path a ball may take when thrown. If we know the formula for the ball's path we can easily trace that path with a graph. Using a spreadsheet to create and print this graph, we can actually "see" the ball "move".