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Author Topic: xD_aQt's Methods Thread  (Read 35756 times)  Share 

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xD_aQt

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xD_aQt's Methods Thread
« on: January 14, 2010, 10:01:33 am »
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I have got no clue where to begin ... :-\

Let f(x) = , The range of f(x) is
« Last Edit: February 01, 2010, 05:31:37 pm by xD_aQt »
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the.watchman

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Re: holiday questions
« Reply #1 on: January 14, 2010, 10:08:49 am »
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The range is

I think the reason for this is that the maximum value of the numerator is 21 (no matter what ) and the minimum value of the denominator is 7 (when ), so the maximum value of is

For the minimum value, the maximum value of the denominator is , so can't equal 0, but approaches 0

Sorry for my bad explaining!!!
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xD_aQt

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Re: holiday questions
« Reply #2 on: January 14, 2010, 10:12:17 am »
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Quote from: the.watchman on January 14, 2010, 10:08:49 am
The range is

I think the reason for this is that the maximum value of the numerator is 21 (no matter what ) and the minimum value of the denominator is 7 (when ), so the maximum value of is

For the minimum value, the maximum value of the denominator is , so can't equal 0, but approaches 0

Sorry for my bad explaining!!!
I guess that sounds about right! :) If someone could clarify?
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the.watchman

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Re: holiday questions
« Reply #3 on: January 14, 2010, 10:13:25 am »
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Sorry, it's actually
My bad!!!
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xD_aQt

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Re: holiday questions
« Reply #4 on: January 14, 2010, 10:15:41 am »
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The function y = -2 cos (3x - ) + 6 has range

« Last Edit: January 14, 2010, 10:20:45 am by xD_aQt »
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xD_aQt

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Re: holiday questions
« Reply #5 on: January 14, 2010, 10:16:10 am »
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Quote from: the.watchman on January 14, 2010, 10:13:25 am
Sorry, it's actually
My bad!!!
Haha, could you explain please?
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the.watchman

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Re: holiday questions
« Reply #6 on: January 14, 2010, 10:17:43 am »
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Quote from: xD_aQt on January 14, 2010, 10:16:10 am
Quote from: the.watchman on January 14, 2010, 10:13:25 am
Sorry, it's actually
My bad!!!
Haha, could you explain please?

The maximum is defined at so it is including the 3
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the.watchman

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Re: holiday questions
« Reply #7 on: January 14, 2010, 10:19:30 am »
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pi is \pi (but it looks dodgy)

Ok, the 'central' point of the cosine graph is at .
As the amplitude is 2, take the values 2 units from in either direction.

SO the range is
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xD_aQt

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Re: holiday questions
« Reply #8 on: January 14, 2010, 10:21:58 am »
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Quote from: the.watchman on January 14, 2010, 10:19:30 am
pi is \pi (but it looks dodgy)

Ok, the 'central' point of the cosine graph is at .
As the amplitude is 2, take the values 2 units from in either direction.

SO the range is
Cheers .. umm so the graph starts from 6? and from there it moves up and down of 2 units? is that right?
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the.watchman

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Re: holiday questions
« Reply #9 on: January 14, 2010, 10:26:16 am »
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It doesn't actually start from because it's cos, but if you have or ,
then the range is
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xD_aQt

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Re: holiday questions
« Reply #10 on: January 14, 2010, 10:30:08 am »
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Quote from: the.watchman on January 14, 2010, 10:26:16 am
It doesn't actually start from because it's cos, but if you have or ,
then the range is
mmm .. think I get you :)
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xD_aQt

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Re: holiday questions
« Reply #11 on: January 14, 2010, 10:34:02 am »
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The range of the function represented by {(x,y): y = x2 + 1, x ɛ [-2,1]} is
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brightsky

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Re: holiday questions
« Reply #12 on: January 14, 2010, 10:40:32 am »
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xD_aQt, for these kinds of questions, just imagine how the graph might look like. where

The graph is essentially a normal parabola moved 1 unit upwards. So the range (how much the graph covers in terms of y-values), starts at 1.

However, the graph is limited . Hence, we need to find the y-value when x = -2 and when x = 1.

Substitute those x-values into the equation:

and

So the range of the graph is . Tell me if I'm wrong...prob you need to limit the graph somehow.
« Last Edit: January 14, 2010, 10:42:57 am by brightsky »
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xD_aQt

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Re: holiday questions
« Reply #13 on: January 14, 2010, 10:42:17 am »
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Quote from: brightsky on January 14, 2010, 10:40:32 am
xD_aQt, for these kinds of questions, just imagine how the graph might look like. where

The graph is essentially a normal parabola moved 1 unit upwards. So the range (how much the graph covers in terms of y-values), starts at 1.

However, the graph is limited . Hence, we need to find the y-value when x = -2 and when x = 1.

Substitute those x-values into the equation:

and

The biggest out of the numbers is 5, so the range of the graph is
Haha, thanks I get you :)
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xD_aQt

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Re: holiday questions
« Reply #14 on: January 14, 2010, 10:46:00 am »
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Could someone explain to me maximal domain, is it basically the domain? .. sorry for all the questions but I haven't got my text yet :P

The maximal domain of the function with equation f(x) = is
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