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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: kenhung123 on March 19, 2010, 11:07:10 am

Title: Addition of ordinates shape prediction
Post by: kenhung123 on March 19, 2010, 11:07:10 am
Is there anyway to predict the shape of the resulting function when adding 2 individual functions together? I mean if you just sub random points in you can't really predict the shape (unless you sub in the right ones by chance)
Title: Re: Addition of ordinates shape prediction
Post by: the.watchman on March 19, 2010, 03:38:27 pm
Well start by plotting major points, then take a look at the functions you're adding.
If you can estimate them as polynomials, then have a think about what the result is likely to be.
If not, then just rely on respective gradients of points

EDIT: 1400 posts :D
Title: Re: Addition of ordinates shape prediction
Post by: TrueTears on March 19, 2010, 03:47:36 pm
Is there anyway to predict the shape of the resulting function when adding 2 individual functions together? I mean if you just sub random points in you can't really predict the shape (unless you sub in the right ones by chance)
don't sub points just add the heights respectively.
Title: Re: Addition of ordinates shape prediction
Post by: the.watchman on March 19, 2010, 04:40:10 pm
Is there anyway to predict the shape of the resulting function when adding 2 individual functions together? I mean if you just sub random points in you can't really predict the shape (unless you sub in the right ones by chance)
don't sub points just add the heights respectively.
Is there anyway to predict the shape of the resulting function when adding 2 individual functions together? I mean if you just sub random points in you can't really predict the shape (unless you sub in the right ones by chance)
don't sub points just add the heights respectively.

Yep, good points to use are:

a) when one is a zero (the height is the point on the other graph at the same x-value)
b) when they are the same (double the y-values)
You can keep adding as many points as you like until you get a good idea of what the shape is :)
Title: Re: Addition of ordinates shape prediction
Post by: the.watchman on March 19, 2010, 04:54:19 pm
Is there anyway to predict the shape of the resulting function when adding 2 individual functions together? I mean if you just sub random points in you can't really predict the shape (unless you sub in the right ones by chance)
don't sub points just add the heights respectively.

You can just... look at it lol?
Add the distances from x axis in your head by inspection!

Yeah, you can do it in your head, but it's nicer to get at least a couple of main points on the page for some idea of scale, yeah?
Title: Re: Addition of ordinates shape prediction
Post by: TrueTears on March 19, 2010, 04:56:48 pm
Is there anyway to predict the shape of the resulting function when adding 2 individual functions together? I mean if you just sub random points in you can't really predict the shape (unless you sub in the right ones by chance)
don't sub points just add the heights respectively.

You can just... look at it lol?
Add the distances from x axis in your head by inspection!
yeah exactly this. you will get an idea of the scale by doing this anyway...
Title: Re: Addition of ordinates shape prediction
Post by: the.watchman on March 19, 2010, 04:59:26 pm
Is there anyway to predict the shape of the resulting function when adding 2 individual functions together? I mean if you just sub random points in you can't really predict the shape (unless you sub in the right ones by chance)
don't sub points just add the heights respectively.

You can just... look at it lol?
Add the distances from x axis in your head by inspection!

Yeah, you can do it in your head, but it's nicer to get at least a couple of main points on the page for some idea of scale, yeah?

I usually just pick the intercepts with axis and each other n shit.

I know, I do it like that too, but I thought it's better to start with the basic tips :D

EDIT: btw, this is not in any way meant to be offensive
Title: Re: Addition of ordinates shape prediction
Post by: the.watchman on March 19, 2010, 05:04:03 pm
Is there anyway to predict the shape of the resulting function when adding 2 individual functions together? I mean if you just sub random points in you can't really predict the shape (unless you sub in the right ones by chance)
don't sub points just add the heights respectively.

You can just... look at it lol?
Add the distances from x axis in your head by inspection!

Yeah, you can do it in your head, but it's nicer to get at least a couple of main points on the page for some idea of scale, yeah?

I usually just pick the intercepts with axis and each other n shit.

I know, I do it like that too, but I thought it's better to start with the basic tips :D

EDIT: btw, this is not in any way meant to be offensive

LOL it's not offensive xD?

Not to you ;)
Title: Re: Addition of ordinates shape prediction
Post by: kenhung123 on March 23, 2010, 06:59:51 pm
Finding the points is not hard its just "guessing" how to graph behaves between the points is hard
Title: Re: Addition of ordinates shape prediction
Post by: the.watchman on March 23, 2010, 07:08:13 pm
Finding the points is not hard its just "guessing" how to graph behaves between the points is hard

It's usually a bit of guesswork, but if it helps, just work out more points, that should help.
Then once you get some more experience, you should be able to spot clear patterns etc.

(Remember, looking at how the graphs are increasing/decreasing can help with the shape)
Title: Re: Addition of ordinates shape prediction
Post by: stonecold on March 23, 2010, 07:15:51 pm
i agree, i struggle so much with this, probably because i don't do spesh.

i only found out what an oblique asymptote was the other day!

are there any limitations to what can be asked, or they can basically pull any two graphs from the methods course, add them, and expect you to draw it.  i hate it!

i like modulus function though :)
Title: Re: Addition of ordinates shape prediction
Post by: TrueTears on March 23, 2010, 08:12:21 pm
Is there anyway to predict the shape of the resulting function when adding 2 individual functions together? I mean if you just sub random points in you can't really predict the shape (unless you sub in the right ones by chance)
don't sub points just add the heights respectively.

HOW DO YOU POSSIBLY GET THE HEIGHTS OF THE OTHER FUNCTIONS UNLESS THEY ARE LINEAR!

THAT WOULD TAKE AGES AND EXTREME PRECISION!
yeh
Title: Re: Addition of ordinates shape prediction
Post by: kenhung123 on March 23, 2010, 08:15:22 pm
He means add the distance from the x axis

Title: Re: Addition of ordinates shape prediction
Post by: Blakhitman on March 23, 2010, 08:19:00 pm
yeah I just kinda judge by eye where the point is...always works.
Title: Re: Addition of ordinates shape prediction
Post by: stonecold on March 23, 2010, 08:22:14 pm
you guys are legends.  now its way easier to do addition of ordinates. just draw the graphs separate and add the displacements form x.  i used to sub in values.  took ages and always got them wrong anyway....

stupid textbook explanations...
Title: Re: Addition of ordinates shape prediction
Post by: the.watchman on March 23, 2010, 08:36:12 pm
you guys are legends.  now its way easier to do addition of ordinates. just draw the graphs separate and add the displacements form x.  i used to sub in values.  took ages and always got them wrong anyway....

stupid textbook explanations...

Haha
Lesson 1: never believe your textbook! :D
Title: Re: Addition of ordinates shape prediction
Post by: Blakhitman on March 23, 2010, 08:38:30 pm
Yeah, my teacher never told us to do anyway except just add the distances of y-values at different x-values and then join the points.

Remember though, when finding difference of functions, you must subtract the right one, e.g f(x)=g(x)-h(x) then you need to get the heights at different x-values of h(x) and subtract them from g(x) at those x-values.

Title: Re: Addition of ordinates shape prediction
Post by: the.watchman on March 23, 2010, 08:39:16 pm
Yeah, my teacher never told us to do anyway except just add the distances of y-values at different x-values and then join the points.

Remember though, when finding difference of functions, you must subtract the right one, e.g f(x)=g(x)-h(x) then you need to get the heights at different x-values of h(x) and subtract them from g(x) at those x-values.



Yup, and you have to be careful about the sign of the resulting function, can be confusing at times!
Title: Re: Addition of ordinates shape prediction
Post by: Blakhitman on March 23, 2010, 08:40:07 pm
What do you mean the sign?
Title: Re: Addition of ordinates shape prediction
Post by: m@tty on March 23, 2010, 08:41:14 pm
Difference of functions can be very daunting, and you will often make errors.

So don't do it.

Instead, in the case of g(x)-h(x), sketch g(x) and -h(x) and add the relative heights.
Title: Re: Addition of ordinates shape prediction
Post by: the.watchman on March 23, 2010, 08:41:45 pm
What do you mean the sign?

Like if it's negative minus negative, then it could be either pos or neg etc.
I know it's not that hard, but be careful, because it could ruin the entire graph

Difference of functions can be very daunting, and you will often make errors.

So don't do it.

Instead, in the case of g(x)-h(x), sketch g(x) and -h(x) and add the relative heights.

I agree :)
Title: Re: Addition of ordinates shape prediction
Post by: Blakhitman on March 23, 2010, 08:43:44 pm
Difference of functions can be very daunting, and you will often make errors.

So don't do it.

Instead, in the case of g(x)-h(x), sketch g(x) and -h(x) and add the relative heights.

omg, Legend! never thought of that...Thanks!
Title: Re: Addition of ordinates shape prediction
Post by: stonecold on March 23, 2010, 08:44:06 pm
oh yeah, forgot you can have subtraction of ordinates lol.
something else for me to learn....

o0o0o0o.  very clever matty.  i shall try it out at some point :)
Title: Re: Addition of ordinates shape prediction
Post by: the.watchman on March 23, 2010, 08:45:09 pm
Just out of interest, has anyone tried sketching composites from the sketched graphs (no eqns)?
I tried it, but it got really complicated :D
Title: Re: Addition of ordinates shape prediction
Post by: m@tty on March 23, 2010, 08:48:16 pm
There is one easy one ;D

Finding f[g(x)]

f(x) can be absolutely anything, and g(x) to be |x| or -|x| ;D Too easy when f(x) is already graphed. :P
Title: Re: Addition of ordinates shape prediction
Post by: the.watchman on March 23, 2010, 08:49:27 pm
There is one easy one ;D

Finding f[g(x)]

f(x) can be absolutely anything, and g(x) to be |x| or -|x| ;D Too easy when f(x) is already graphed. :P

Yes indeed
I mean wacky functions (not necessarily having a sane eqn :P)
You can do addition easy sure, but composite is killer
Try some!
Title: Re: Addition of ordinates shape prediction
Post by: Blakhitman on March 23, 2010, 08:50:11 pm
You went to the free TSFX lecture didnt you the.watchman? the lecturer explained a good way of doing it there...shame it was pretty complicated and I probably don't understand it now *scratch*
Title: Re: Addition of ordinates shape prediction
Post by: TrueTears on March 23, 2010, 08:50:39 pm
kamil taught me a pretty sweet way back in yr 12... maybe i shud get him to explain 1 sec...
Title: Re: Addition of ordinates shape prediction
Post by: the.watchman on March 23, 2010, 08:50:47 pm
You went to the free TSFX lecture didnt you the.watchman? the lecturer explained a good way of doing it there...shame it was pretty complicated and I probably don't understand it now *scratch*

Erm, no...
I didn't go to the TSFX lectures
Title: Re: Addition of ordinates shape prediction
Post by: m@tty on March 23, 2010, 08:53:25 pm
That would be almost impossible, you would have to get a ruler out and find the height of the second where the distance from the x-axis is the same as the height of the first -- and then plot this point in line with the point you took from the first above the x-axis....

ahhh, ugly.. Where did you get these questions? ??
Title: Re: Addition of ordinates shape prediction
Post by: the.watchman on March 23, 2010, 08:57:56 pm
That would be almost impossible, you would have to get a ruler out and find the height of the second where the distance from the x-axis is the same as the height of the first -- and then plot this point in line with the point you took from the first above the x-axis....

ahhh, ugly.. Where did you get these questions? ??

Dr He... :P
He only did a quick demo for fun :)