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What's the range of this function?

The function is f(x) = (2e^3x ) -1

I think the range is any real number, am I right?
No. What's the range for exe^x? What about e3xe^{3x}? They're the same. Now what about 2e3x2e^{3x}? Translate this answer down by 1 and you got it.

Range is certainly never ALL real values with an exe^x graph.
(edited 7 years ago)
Reply 2
Avatar for B_9710
B_9710
18
Solve f(x)=-1
consider e^x and the transformations needed to get to f(x), knowing that there is an asymptote at the x axis on the curve y=e^x .
Reply 4
Avatar for TSR George
TSR George
OP
17
Original post by RDKGames
No. What's the range for exe^x? What about e3xe^{3x}? They're the same. Now what about 2e3x2e^{3x}? Translate this answer down by 1 and you got it.

Range is certainly never ALL real values with an exe^x graph.


e^x has a range of all positive numbers right?
Reply 5
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B_9710
18
No, exp(x)>0.
If so, solve ex=0e^x=0 for me.
Reply 7
Avatar for Zacken
Zacken
22
Original post by B_9710
No, exp(x)>0.


Original post by RDKGames
If so, solve ex=0e^x=0 for me.


Positive numbers don't include 0, which is why the term "non-negative" exists. So yes, he is right.
Reply 8
Avatar for TSR George
TSR George
OP
17
Original post by Zacken
Positive numbers don't include 0, which is why the term "non-negative" exists. So yes, he is right.


Yay! haha! So the 2 in the original question adjusts the range because if e^x had a smallest value of 1 (just for example) then the smallest range value when multiplied by 2 would be 2 right?
sort of right, sort of not
Reply 10
Avatar for Zacken
Zacken
22
Indeed!
Original post by Zacken
Indeed!


And then the -1 moves it down by one so the range is any number bigger than -1?
Original post by RDKGames
If so, solve ex=0e^x=0 for me.


how do I write equations like that?
Reply 13
Avatar for Zacken
Zacken
22
Correct. :smile:
Original post by KnowledgeIsBest
how do I write equations like that?


Latex.

http://www.thestudentroom.co.uk/wiki/LaTex
Reply 15
Avatar for B_9710
B_9710
18
Original post by Zacken
Positive numbers don't include 0, which is why the term "non-negative" exists. So yes, he is right.


Didn't notice the word positive in there.

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