# Range of a Function (P2)

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Thread starter 16 years ago
#1
How do you find the range of a function? I can't remember how to do this at all and the exam's on friday!!

Anyone?!?!?!!
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16 years ago
#2
I can't really explain, but toss me a question and I'll try my best.
0
16 years ago
#3
Put in your values for the domain. Eg. f(x) = 2x - 3, 0 <= x =< 6,
find the values of f(0) and f(6) and there's your range.
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16 years ago
#4
Originally posted by Unregistered
Put in your values for the domain. Eg. f(x) = 2x - 3, 0 <= x =< 6,
find the values of f(0) and f(6) and there's your range.
Your method doesn't always work. In fact it only works (in general) for linear increasing functions. For example consider the function f(x) = x^2 defined over the domain -6 <= x <= 2. Using your method we would then say the range is f(-6) <= f(x) <= f(2) and thus 36 <= f(x) <= 4, which is obviously an invalid statement. Finding the range does involve a bit of thinking about the question you're dealing with. In this question, the range would be 0 <= f(x) <= 36.

Regards,
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16 years ago
#5
That's the only way we were taught..
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16 years ago
#6
Originally posted by Unregistered
That's the only way we were taught..
I'm not sure what's on the P2 syllabus with regard to finding the range of functions, but if it's only the range of linear increasing functions, then your method's fine.

Regards,
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16 years ago
#7
If a function is not linear then you can differentiate it and use the fact the dy/dx = 0 at a stationary point. This does involve a little investigation to see if you have found only one min/max in your domain. Also you can look at the nature of the line as x tends to +- infinity or to the upper/lower limit.

I.e 2/(x+1) Domain R+

As x tends to 0 R tends to 2,
As x tends to infinity R tends to 0 .

So 0<y<2 in this case as the domain was limited

For X^2 - 4x + 7: Domain R

Complete square:

(x-2)^2 - 4 + 7

Since bracket always positive implies minimum at x= 2 of y= 3

So 3<=y<infintiy

Hope these help. Dan

Finally you could complete the square of a quadratic and solve it to get the minimum. It really depends

a) On the function in question
b) The domain, is it specific or is it the reals etc.

Once you have this you can investigate the nature of the curve as needed.
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16 years ago
#8
well, domain is easy to find, range is hard

so you find the inverse of the function and find that domina, an dthat is the range of the function

domain of f`(x) = range of f(x)
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