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Mathematics 22 Online
OpenStudy (anonymous):

y=e^(-x)-e trying to find the range.

OpenStudy (jamesj):

Waht's the range of \( e^x \) ?

OpenStudy (jamesj):

What's

OpenStudy (anonymous):

not sure

OpenStudy (anonymous):

I think 1

OpenStudy (anonymous):

or 0

OpenStudy (jamesj):

Ah ... go back to your class notes or text book and figure it out. Otherwise you'll never be able to answer this question. No, {1} is not the range of e^x, nor {0}

OpenStudy (jamesj):

Once you know that range of e^x, find the range of e^(-x); then the range of e^(-x)-e

OpenStudy (jamesj):

You should definitely learn what the graph of y = e^x looks like. It's a very important function.

OpenStudy (anonymous):

e\[ e ^{1}=e\]

OpenStudy (mertsj):

Also you should know that e is a positive number and a positive number raised to ANY power is positive. So the range of y = e^x is the real numbers greater than 0

OpenStudy (anonymous):

so where this is raise to a neg x does that mean it is all neg. numbers

OpenStudy (jamesj):

\[ y^{-1} = 1/y \]

OpenStudy (jamesj):

Hence if the range of e^x is all positive numbers, the range of e^(-x) is the reciprocal of all positive numbers, which is .....

OpenStudy (mertsj):

NO!!!!!!!!! A positive number raised to ANY POWER AT ALL-POSITIVE, NEGATIVE, OR 0 IS POSITIVE!!!!!!!

OpenStudy (jamesj):

You really should look up the graphs of these functions. So important.

OpenStudy (anonymous):

i did i need to understand how to find it after looking at the graph

OpenStudy (anonymous):

Please be patient I am just learning this sorry

OpenStudy (mertsj):

So is the problem that you aren't quite sure what is meant by the term "range"?

OpenStudy (anonymous):

yes

OpenStudy (mertsj):

So I am going to draw you a picture and see if we can clarify.

OpenStudy (mertsj):

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