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# What's the range of this function?

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

I think the range is any real number, am I right?
2. (Original post by Blake Jones)
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 ? What about ? They're the same. Now what about ? Translate this answer down by 1 and you got it.

Range is certainly never ALL real values with an graph.
3. (Original post by Blake Jones)
The function is f(x) = (2e^3x ) -1

I think the range is any real number, am I right?
Solve f(x)=-1
4. (Original post by Blake Jones)
The function is f(x) = (2e^3x ) -1

I think the range is any real number, am I right?
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 .
5. (Original post by RDKGames)
No. What's the range for ? What about ? They're the same. Now what about ? Translate this answer down by 1 and you got it.

Range is certainly never ALL real values with an graph.
e^x has a range of all positive numbers right?
6. (Original post by Blake Jones)
e^x has a range of all positive numbers right?
No, exp(x)>0.
7. (Original post by Blake Jones)
e^x has a range of all positive numbers right?
If so, solve for me.
8. (Original post by B_9710)
No, exp(x)>0.
(Original post by RDKGames)
If so, solve for me.
Positive numbers don't include 0, which is why the term "non-negative" exists. So yes, he is right.
9. (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?
10. (Original post by Blake Jones)
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
11. (Original post by Blake Jones)
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?
Indeed!
12. (Original post by MathMoFarah)
sort of right, sort of not
Hmm, okay, how should I approach this?

I'm getting confused haha!
13. (Original post by Zacken)
Indeed!
And then the -1 moves it down by one so the range is any number bigger than -1?
14. (Original post by RDKGames)
If so, solve for me.
how do I write equations like that?
15. (Original post by Blake Jones)
And then the -1 moves it down by one so the range is any number bigger than -1?
Correct.
16. (Original post by KnowledgeIsBest)
how do I write equations like that?
Latex.

http://www.thestudentroom.co.uk/wiki/LaTex
17. (Original post by Zacken)
Correct.
Thank you!
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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