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How is somebody going to know enough to zoom in closer, if they "think" there is only one solution because the graph shows one crossing of an axis. What if another solution is off in +infinity? From my hauntings of the physics newsgroup, one the key tasks in any study is to take great care in identifying boundary conditions.

I get the sense that structures and materials deals with these all the time. And any kind of dynamics has to be able to "see" the whole graph in all analyses. The problem with a calculator-generated graph is that nobody looks at the pieces that are off the screen.

Yes. A sine wave is usually only 360degrees "long". Graph paper forces you to know that there are more pis after 2pi.

In the beginning. You don't want all kiddies getting the short cut burnt in first and have to remember the real stuff later.

Yes. And there can be all kinds of other scales.

Yes. Now graph it using different scales. The choice of scaling of a graph is more important than the graph. It can be used to convey information at a glance.

You just demonstrated my point.

My second lesson about the concept of infinity came with graphing on paper by hand.

They learn the buttociation between the math and the picture.

I had absolutely no knowledge that the words linear algebra existed when I was given that coding buttignment. Matrix arithmetic was used in businesses forever. Here's a problem example from the book:

A daily record is kept at the foreign exchange window of a bank. The till collects pounds, liras, francs, pesos, and marks. It is desired to set up a matrix product that gives the value in dollars of the daily accumulation of foreign currency.

Price lists require matrix computations.

BAH