Wednesday, October 3, 2007

Reciprocal Graphs

So lets get this over and done with already...

First of Mr. K gave us some fractions and decimals and we needed to get the Reciprocal. Easy enough eh?

Next he told us that this was going to be the hardest part of this unit. So I hope you all were paying attention to his teachings. Anyways I'll stop typing useless nonsense and start the scribe.

You remember the fractions and decimals he gave us and that he needed to find the reciprocal? Well here's some "notes" that I hope will help you if needed.

As the sequence gets bigger the reciprocal gets smaller.
As the sequence gets smaller the reciprocal gets bigger.
If negative then it gets bigger negatively.
1 is special - reciprocal does not change, Invariant. Invariant means it does not change.

All that was just to help with reciprocals.
Now here are some "notes" on graphing the reciprocal functions. I don’t really get that chart thing he showed us so this is what I can recall during class. Now this is what we really did in class.

Graph the outputs reciprocal, the Y coordinates, not the X coordinates.
Everywhere the outputs = -1 and 1 on the original graph it will be the same on the reciprocal graph.

Steps to graphing... Example: Graph 1/(2-x)

Well first just go and change the equation if that helps 1/(2-x) => 1/(-x+2)

1/(-x+2) => (-x+2)/1 or (-x+2) <====you know how that happened right? Just flip it to get it like that. Now that you have that done, graph this one so it will make things much easier. 1.Graph the original one first.... the reciprocal of the function they give you or the one that isn't in fraction state.

2. After you have the graph done like the one above, get the points that will stay the same. You remember which ones they were right? Where the outputs (y- coords) equal 1 and -1 will always be the same on both graphs.

3. The graph shows you the points in red. Now that you have that done lets get the Asymptote. Of coarse you can just double click it to find out what it is but since im doing this... Asymptote - it is a line on the graph that the graph will never actually touch, but the graph will continue to move towards it.

In our case the asymptote is the root(s). Why? Because when you input the x coord. you get a zero. You can't have a reciprocal of zero... anything over zero is undefined and it just can’t happen.

4. So now you have the graph above. Your two pints and your asymptote should be on there. Now you want to actually plot the graph. On the graph the red dots show you your two points that are always the same. Lets start with the right most point.

You see the point is near the asymptote. Between it and the root on the asymptote you can determine how the graph will look. The graph is going downwards from the asymptote. The x-coords are getting bigger so the reciprocal is it getting smaller. The y-coords are getting bigger negatively so the reciprocal of that is getting smaller negatively.

How do you do that? The x coords need to get smaller so it needs to go downward to get smaller, just along the asymptote. Not along the x axis as the x coords won't be getting smaller. The y coords are getting bigger negatively so it needs to get smaller negatively. This leads it to go along almost touching the x-axis. Not along the asymptote as the y coods would just get bigger negativly again. I know it’s a bit confusing. :S

As you can see it works out fine. The x coords are getting smaller and the y coords are getting bigger negativly

Now finish it off with the other half of the graph. You should be able to do it now right? I don’t know if all these things are correct but if you want to, go ahead and correct me. Don’t quote me on any of this xD

Some things that you need to know…
-Never have your graph curve back
-Don't have the graph touch the Asymptote.

This is basically what you do when you do a problem like this. I hope this scribe helped you guys out at least a little.

Go ahead and correct me on anything you see wrong.

Okay for homework we have...Exercies 10 but Mr. K didn't stop us there. He also gave us the job of finding the Reciprocal graph of the inverse trig functions. So that means we need to get the reciprocal of the graph SEC, CSC, and COT.

Oh yeah the next scibe is wendy. >_> Could you update the list Mr. K?

1 comment:

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