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1. Anyone know the quickest way to find the range of this graph? Would anyone care to explain it to me?
2. What is the minimum value that e^(2x) takes? What is the maximum value that e^(2x) takes? Once you have decided on the answers to those questions, you should be in a better position to find the range of f.
3. (Original post by Kolya)
What is the minimum value that e^(2x) takes? What is the maximum value that e^(2x) takes? Once you have decided on the answers to those questions, you should be in a better position to find the range of f.
0......? i think it's 0. I don't know the answers...thats why i created this thread for anyone to help me? i thought it was all values but i was wrong.
4. (Original post by jj.)
0......? i think it's 0. I don't know the answers...thats why i created this thread for anyone to help me? i thought it was all values but i was wrong.
OK, if you think it's 0: what value of x gives you e^(2x) = 0 then?
5. (Original post by Kolya)
OK, if you think it's 0: what value of x gives you e^(2x) = 0 then?
i dont know i dont understand. how do i do this? if its one mark, there must be an easy way? its not in the textbook either
6. it's the y = ex graph shifted down by -k, so it'll be asymptotic to y = -k, and the range will be y > -k
7. The range basically means: what values can Y take?

For the graph of y= e^x, the asymptote is y = 0. When the graph of that is translated to e^x - k, the -k translates the graph downwards, but we don't know what K is, so therefore, the range is f(x) > -k.
8. (Original post by BrightGirl)
it's the y = ex graph shifted down by -k, so it'll be asymptotic to y = -k, and the range will be y > -k
Oh yeahhhhhhhhh, I forgot about the e^x graph and it's asymptote! argh! thank you!!!
9. (Original post by jj.)
i dont know i dont understand. how do i do this? if its one mark, there must be an easy way? its not in the textbook either
Draw a graph of g(x) = e^(2x) and tell me what the lowest value that g(x) takes is on the graph, and what the highest value that g(x) takes on the graph. If you don't understand the nature of g(x) = e^(2x), you aren't going to be able to understand the nature of f(x) = e^(2x) - k ...!
10. (Original post by jj.)
Oh yeahhhhhhhhh, I forgot about the e^x graph and it's asymptote! argh! thank you!!!
no problem!
11. (Original post by Kolya)
Draw a graph of g(x) = e^(2x) and tell me what the lowest value that g(x) takes is on the graph, and what the highest value that g(x) takes on the graph. If you don't understand the nature of g(x) = e^(2x), you aren't going to be able to understand the nature of f(x) = e^(2x) - k ...!
no worries, i understand now!
12. The range is the lowest and highest values y can take for f = e^2x - k.

What's the lowest value of y?
Well, look at the diagram. It appears to be when x becomes large and negative, right|? As this happens e^2x tends to 0, leaving just -k. WHich is the lower limit of the range.

What's the highest value of y? Well, it doesn't seem to have a limit because you can plainly see it's going up and up. So what's the range?

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