Getting the Most from Graphing Calculators


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.


CALCULATOR FAQ's

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.

List of questions on this page.


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.

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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 x = -1, a look at the graph on a scale between -2 and 1 will reveal that something is wrong.

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.

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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 x = 1, the calculator will discover that the values of f near to 1 become very large. The calculator will then draw a spike at x = 1, and this often looks like an asymptote on the display. This is a bug, not a feature.

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Could the graph I see be completely wrong?

Sadly, yes. There are two reasons.

  1. USER ERRORS: We all make mistakes. Common mistakes made when graphing functions are:

    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.

  2. DESIGN CHARACTERISTICS: It is rare, but it can happen that a graphing calculator displays an extremely misleading graph. One cause is numerical precision. If the calculation needed to determine the y-coordinate of a point on a graph exceeds the precision of the calculator, the results will be unpredictable. Another cause is the calculator's display. The calculator (or computer acting as a calculator) displays graphs on a screen made up of tiny dots called pixels. Once a scale is set, each pixel actually represents a small range of values. The graph of a function cannot show large changes in the function value over this range.

    List of questions on this page.


    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.

    List of questions on this page.


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