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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: pinklemonade on February 09, 2015, 08:27:30 pm

Title: Addition of Ordinates??
Post by: pinklemonade on February 09, 2015, 08:27:30 pm: Hey,
I honestly do not understand addition of ordinates at all and was wondering if anyone knew any helpful websites or links that could help me get a better understanding

Thank you!
Title: Re: Addition of Ordinates??
Post by: nerdmmb on February 09, 2015, 08:29:22 pm: Quote from: pinklemonade on February 09, 2015, 08:27:30 pm
Hey,
I honestly do not understand addition of ordinates at all and was wondering if anyone knew any helpful websites or links that could help me get a better understanding

Thank you!

Ordinates simply mean the y-values. So when you're wanting to add ordinates, you're basically adding the y-values to produce the new graph, being mindful of any asymptotes.
Title: Re: Addition of Ordinates??
Post by: Gentoo on February 09, 2015, 09:00:04 pm: When you're sketching the addition of two existing graphs (that are already sketched for you on the axes), use any points where one of the two graphs hits the x-axis, or where the two graphs intersect, as starting points to sketch your addition of ordinates graph. It's very easy to gauge the y value of the addition of ordinates graph (in the case of the former, it's exactly where the graph that hasn't intersected the x-axis is, and in the case of the latter it's just doubling the distance from the x-axis). Coming from someone who had to put a lot of effort into drawing graphs (i'm not a good artist), it helps to have some reference points before you start sketching the whole thing. The gradient of the addition of ordinates graph can be tricky to accurately represent too. Just take your time.

Also on a related note, if you're adding two circular functions together, the period of the addition of ordinates graph is the lowest common denominator of the periods of the two initial graphs. Say the period of one is 3pi (e.g. sin(2x/3), and the period of the second is 2pi (e.g. cos(x)), the period (the range of x values before the whole graph repeats itself) of the addition of ordinates graph will be 6pi.
Title: Re: Addition of Ordinates??
Post by: pinklemonade on February 09, 2015, 10:05:11 pm: What about if theres 3 graphs you need to sketch?

At the moment I'm trying to sketch $y=2x-\frac{2}{(x+2)}+\frac{1}{(x-3)}$
and I have no idea how to! :-\
Title: Re: Addition of Ordinates??
Post by: Gentoo on February 09, 2015, 10:26:14 pm: Are the graphs of each of those terms on their own sketched for you on the same pair of axes? Is this a calculator active question? Asking you to sketch a 3-term relation like that without the aid of a calculator or with each term already sketched is not something that would really happen in a SAC or exam, so I wouldn't worry. It would be ridiculously time consuming, at the very least.

If you needed to do it with no prior info or a calculator, you'd just sketch each term on its own then try and add the y values of each graph at all points to produce the addition of ordinates graph. There's no golden rule to doing so, butyou can use the techniques I mentioned in my previous post to make it a little easier (though with a 3 term graph, even they probably won't help that much).
Title: Re: Addition of Ordinates??
Post by: 99.90 pls on February 20, 2015, 02:08:00 am: The best way to sketch these is just to consider what value y approaches as x approaches positive infinity, negative infinity and asymptotes from both the left side and right side. Just remember that in general:

1/infinity -> 0
1/0 -> infinity

Use addition of ordinaries when it gets iffy and you're pretty much set for any graph/function they give you.
Title: Re: Addition of Ordinates??
Post by: just_jordan on March 14, 2015, 04:28:16 pm: Quote from: pinklemonade on February 09, 2015, 10:05:11 pm
What about if theres 3 graphs you need to sketch?

At the moment I'm trying to sketch $y=2x-\frac{2}{(x+2)}+\frac{1}{(x-3)}$
and I have no idea how to! :-\

Usually for these questions it's best to consider three things:

1. Asymptotes: so when the equation you are given is undefined, usually for something like a/(x-b), x=b is one and you can find for any amounts of vertical asymptotes. As for oblique asymptotes, anything but the 'hyperbola/truncus' terms will be the oblique asymptote.

2. As x approaches these asymptotes: Usually you want to know what the y-value is as x approaches an asymptote, or +ve and -ve infinity so you can get a grasp of where to start in terms of drawing the graph. Almost always the y approaches positive or negative inifity as x approaches an asymptote

3. Intercepts: To find y-int just sub x=0 and vice versa.