Your graphing calculator is a powerful tool. It can save you a lot of work if used properly but give you misleading information if misused. The FAQ list on this page will help you make the best use of your calculator. If there are other items which should be added, please let us know by email.
Note: This is NOT a "how-to" manual which tells you what to push in order to do calculations or generate graphs. Opportunities to learn the use of a graphing calculator are offered on a section-by-section and institution-by-insitution basis.
|The answer is 1/3. Is .333 correct? Can I solve equations using my calculator? Can I use graphs to check answers? Does my calculator show asymptotes on graphs? Could the graph I see be completely wrong? What are the dangers of using really small numbers?|
The answer is 1/3. Is .333 correct? No. The exact value of.333 is 333/1000 which is not the same as 1/3. In applying mathematics to physical reality, it suffices to work with good approximations. For many purposes .333 is just as good as 1/3. But they are not equal.
Can I solve equations using my calculator? Yes and no. Many hand-held calculators have built in "solvers". You can also use a graphing calculator to "see" where a function f(x) crosses the x-axis, thereby "solving" f(x)=0. But all calculations are limited by the precision of the calculator, and there are further limits to the accuracy of visual conclusions. Be aware that the solutions you obtain are approximations and that other methods must be used to get exact or symbolic answers.
Can I use graphs to check answers?Absolutely! Graphs can be effectively used to check for errors in algebraic calculations. For example, if you have erroneously computed that x2+ x + 1 has a zero at
We will use Calculus to draw conclusions about the behavior of functions. As an example, we will be interested in knowing when a functions is increasing or decreasing. This behavior is evident from a graph, so a graph can and should be used to check our conclusions.
Does my calculator show asymptotes on graphs?
It shouldn't. But when graphing a function such as f(x) = 1/(x-1)2, which is undefined and has an asymptote at
Could the graph I see be completely wrong?
Sadly, yes. There are two reasons.
TO AVOID USER ERRORS, WORK CAREFULLY AND TAKE TIME TO DOUBLE-CHECK WHAT YOU DO UNDERSTAND AND ASK OR READ ABOUT WHAT YOU DO NOT UNDERSTAND.
What are the dangers of using really small numbers?
You will get complete garbage if your calculations involve numbers smaller than the precision of your calculator. What makes this truly insidious is that sometimes a calculation involves really small numbers in a hidden way. For example, if you are attempting to compute the value of sin(x3)/x3, then a small number will be CUBED before sine is evaluated. This cubing makes the number even smaller. So to compute with numbers as small as 10-6, you will need a calculator which can handle numbers as small as 10-18.
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William A. Bogley