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Mth163
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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The basic exponential function
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http://vhcc2.vhcc.edu/pc1fall9/synopsis.htm
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If k is negative the function is also reflected about the y axis so that it becomes asymptotic to the positive t axis.
in your sentence did you mean reflected about the negative y axis, because it its asymptotic to the positive t axis but on which side???
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Comparing e^(k t) with e^(-k t):
If we replace t by -t, e^(-k t) becomes e^(k t).
This means that the value of e^(-k t) for a given t is the same as the value of e^(k t) for the opposite value of t, meaning the value of t on the opposite side of the y axis.
As a concrete example,
if t = 3 then
e^(2 t) = e^6
If t = -3 then
e^(-2 t) = e^6.
So the graph of e^(2 t) includes the point (3, 6), and the graph of e^(-2 t) includes the point (-3, 6).
These points are reflections of one another about the y axis.
Any point (t, y) on the graph of e^(k t) is the reflection of the point (-t, y) on the graph of e^(-k t).
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