C3 help, finding range of a function... positive rep.

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ND6
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#1
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Hey, please can somebody lead me to or explain a very good method for finding the range of a function.

Thanks.
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jonny23563
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You just have to think about it. Start from the bottom (natural numbers) and work upwards until one of them doesn't work.
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ND6
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(Original post by jonny23563)
You just have to think about it. Start from the bottom
(natural numbers) and work upwards until one of them doesn't work.
what about negative numbers where would i start from?
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Topmanfaz
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Buy a graphical calculator..
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jonny23563
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Well negative numbers are part of Z, so you just need to think whether the function is defined for them. e.g. a classic example is square roots, which only work for R+ (A-level assumes no knowledge of complex numbers, does it?).
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ND6
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(Original post by jonny23563)
Well negative numbers are part of Z, so you just need to think whether the function is defined for them. e.g. a classic example is square roots, which only work for R+ (A-level assumes no knowledge of complex numbers, does it?).
no i don't think it does. thanks!
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jonny23563
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No problem, I'm sorry I couldn't be more help, but the only advice really is just "think about it!".
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scott8anthony
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Would differentiating and equating to zero help? (i.e. finding maximum and minimum values) :confused:
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lujamil
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if there is a square in the equation then there round be no negatives in the range because squaring a negative makes positive... simple?
range of a function is the domain of the inverse of the same function =] another point that may help =]
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Stex Bomb
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(Original post by ND6)
Hey, please can somebody lead me to or explain a very good method for finding the range of a function.

Thanks.
Man I used to struggle so much with range!

But now I've sussed it!

Basically, use your graphical calculator to draw it out, its the easiest way.

Take y=x² for example.
Draw it out using a graphical or using a table (working out what y is with respect to x)

The domain for it is xER (x can take any real value as it is continuous)

Image

When looking at range, we look at the y axis and what values we can get out of the function.

In this case, the graph ends when y = 0 and therefore the range is

f(x) = > 0
..........¯

Hope this helps

Basically, look at the y axis values when you're finding range and x axis when finding domain.
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HeadmasterCid
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(Original post by ND6)
Hey, please can somebody lead me to or explain a very good method for finding the range of a function.

Thanks.
Easiest way is to draw a sketch to visualise it. You may need to calculate some features of the sketch (turning points being the most likely here), but you should be able to work it out from there.

If you can't sketch  y = f(x) then work out  f^{-1} (x) . If you can sketch the inverse then it is easy to sketch the original function as it is just a reflection in the line  y = x , but you might not even need to sketch the original function as the domain of the inverse should just be the range of the original function.

Be careful when sketching the inverse though as the domain of the original function may have been restricted, and this will mean the domain/range of the inverse is also restricted.

For example, let's say you don't know how to sketch square root graphs, and you've been asked to find the range of  f(x) = \sqrt{x - 4} , with domain  x \geq 4 . You can easily work out the inverse function,  f^{-1} = x^2 + 4 , and this is really easy to sketch (a parabola with minimum at  (0,4) . If you reflect this in the line  y = x then you will have an idea about what the graph needs to look like, BUT YOU HAVE TO BE CAREFUL as this isn't quite correct. You need to remember that the square root symbol means positive square root only, and so you only want the portion of the sketch above the x-axis. This tells you that the range must be  f(x) \geq 0 .

That example is about as complicated as it gets in A-level Maths.
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davros
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(Original post by HeadmasterCid)
Easiest way is ...

.
Please don't resurrect EIGHT YEAR OLD threads! The OP will be long gone by now
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HeadmasterCid
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(Original post by davros)
Please don't resurrect EIGHT YEAR OLD threads! The OP will be long gone by now
Oh, I didn't even notice! It came up in 'Latest discussions' for some reason!
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