Discussion:  Traffic Jam Applet tool 
Topic:  evaluating x^c 
Related Item:  http://mathforum.org/mathtools/tool/10/ 
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Subject:  RE: evaluating x^c 
Author:  Mathman 
Date:  Sep 27 2004 
> I'm interested in how most K12 teachers expect this expression to
> be evaluated... as (x)^c or as (x^c). Using the TI83 there seems
> to be some inconsistency between graphing and evaluating.
For
> instance, if I type in the expression 3.8^2.1 I get a response to
> be
16.502... Yet when I try to graph x^2.1 the graph is only
> defined for positive x.
The manner in which figures and operators are typed into a calculator has to do
with the operation of that calculator, and not to do with order of operations or
unary operators. A RPN [Reverse Polish Notation] calculator would require a
different order of keypress. The *mathematical* definition requires that a
negative sign preceding any quantity negates it. When brackets are used, the
quantity inside the brackets preceded by a negative will negat that quantity,but
not necessarily the entire expression.
For positive x, then ...
x is negative [x<0]
(x) is also negative.
x^n is negative for all n, even or odd.
(x)^n is negative for ODD n, and positive for EVEN n.
The first example of the last two has only one negative to consider. The last
has "n" negatives multiplied together.
The problem then is to learn which order of keypresses produce the expected
values, not the other way around. The gearshift might be in a different place
in a car, but if you want to go forward you must learn to operate that car.
I've done a lot of spreadsheets, and much of the work is "workaround", learning
to use available functions as they exist to produce desired results.
A last comment: To negate a value on a calculator, use the (+) key, not the
() key. The first expresses a negative number, and trhe second the
subtraction operator. Usually the (+) is performed last in a term in order
to negate any preceding kepyressed or calculated value.
David.
 
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