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Core 3 June 2006

Hi, I was doing a past paper question and when it came to question 8 on the Core 3 June 2006, I got confused with the mark scheme. It is asking for the range of the function f and I put f(x) must be greater or equal to zero but the mark scheme says it must be greater than minus one. How is this different? I attached images of the question and the mark scheme. Thanks ImageUploadedByStudent Room1413728183.658559.jpg
ImageUploadedByStudent Room1413728224.211824.jpg


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Original post by Heartland
Hi, I was doing a past paper question and when it came to question 8 on the Core 3 June 2006, I got confused with the mark scheme. It is asking for the range of the function f and I put f(x) must be greater or equal to zero but the mark scheme says it must be greater than minus one. How is this different? I attached images of the question and the mark scheme. Thanks


Your answer is incorrect because f(x) can be less than 0
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Heartland
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But I'm saying its greater or equal to zero... I don't get it, can you explain it please?


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Original post by Heartland
But I'm saying its greater or equal to zero... I don't get it, can you explain it please?



Yes I know you are - that is why you are incorrect

What if x is a negative number
Reply 4
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Heartland
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I still don't get it. My range doesn't say that x is a negative?


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Original post by Heartland
I still don't get it. My range doesn't say that x is a negative?


Please use the reply button


The domain was all real x
If x is negative then f(x) is also negative, but greater than -1
Original post by Heartland
I still don't get it. My range doesn't say that x is a negative?


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I also got stuck on this question.
The way my teacher explained it to me it that you know the graph of "e" is > 0 but then the -1 (from the question) is a transformation, so the whole graph shifts downwards, that's where > -1 comes in.
Hope that helps (:
Reply 7
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Heartland
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Original post by Roxanne18
I also got stuck on this question.
The way my teacher explained it to me it that you know the graph of "e" is > 0 but then the -1 (from the question) is a transformation, so the whole graph shifts downwards, that's where > -1 comes in.
Hope that helps (:


Ok so if the graph had -3 on the end the range would be >-3? Thanks


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(edited 9 years ago)
Original post by Heartland
Ok so if the graph had -3 on the end the range would be >-3? Thanks


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As long as there were no other transformations and it was still an "e" graph then yes I think it would (:
Original post by Heartland
Ok so if the graph had -3 on the end the range would be >-3? Thanks



Do you understand why?
Reply 10
Avatar for davros
davros
16
Original post by Heartland
Hi, I was doing a past paper question and when it came to question 8 on the Core 3 June 2006, I got confused with the mark scheme. It is asking for the range of the function f and I put f(x) must be greater or equal to zero but the mark scheme says it must be greater than minus one. How is this different? I attached images of the question and the mark scheme. Thanks ImageUploadedByStudent Room1413728183.658559.jpg
ImageUploadedByStudent Room1413728224.211824.jpg


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The range of the function gives you the set of values that the function can output.

As x gets very big and negative, 2e3x2e^{3x} gets smaller and smaller - very close to 0. So 2e3x−12e^{3x} - 1 can be as close to -1 as you want but not actually equal to -1. Therefore the range has to be all values > -1.
Reply 11
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Heartland
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Ok I get it now thanks everyone


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