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Math Help - Graph Transformation

  1. #1
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    Graph Transformation

    Hello!

    I have an assignment to do in maths and I've encountered some problems. The teacher I have is not very helpful so I hope that I'll receive some help from here instead. Basically, we have to design a function to fit these variables:

    x 1.7 2.0 2.9 4.1 5.6 6.3 7.0 8.0 10.0 13.9
    y 42.0 21.0 10.3 6.8 5.1 4.8 4.4 4.1 3.7 3.2

    First I thought of using a simultaneous equation to solve for a and c by using this formula: y = a(1/x)+c... but it ended up weird and I'm not sure of what x and y variables to use... I'm not even sure of the formula I came up with. So, well, what to do? I know that many possible ways can be used to create an appropriate graph to fit the variables and one of them is supposed to be by simultaneous equations which I personally prefer as I cannot handle complex maths. Guided help would be kind as I am to describe the process and such.

    Thank you! (:
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  2. #2
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    What was the appearance of your Normal Equations? I'll suggest one. Youtell me the other.

    \sum{y} = a \cdot \sum{\frac{1}{x}} + c \cdot N

    N = 10, of course.
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  3. #3
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    Quote Originally Posted by TKHunny View Post
    What was the appearance of your Normal Equations? I'll suggest one. Youtell me the other.

    \sum{y} = a \cdot \sum{\frac{1}{x}} + c \cdot N

    N = 10, of course.
    I'm sorry, but I really do not understand your question? The variables gives an exponential curve, if that is what you are asking for. Where did you get N from and what am I supposed to do with the formula?

    Sorry for being so... dumb.
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    Quote Originally Posted by Fifi View Post
    I'm sorry, but I really do not understand your question? The variables gives an exponential curve, if that is what you are asking for. Where did you get N from and what am I supposed to do with the formula?

    Sorry for being so... dumb.
    How many numbers do you have? That is N.
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    Quote Originally Posted by TheMasterMind View Post
    How many numbers do you have? That is N.
    10. 20 in total, but 10 dependent on the independent 10 others.
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    Oh sorry, my mistake. Thought you were asking me. But.. how do I continue now and what change does it make taking c times the number of numbers I have?
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  7. #7
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    "y = a(1/x)+c... "

    Without some background in the calculus, this is a very difficult task. You may be left with simply guessing. Pick values for 'a' and 'c' tha tmake sense and adjust them to see what happens. You should be able to do this in MS Excel with reasonable accuracy.
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    Quote Originally Posted by TKHunny View Post
    "y = a(1/x)+c... "

    Without some background in the calculus, this is a very difficult task. You may be left with simply guessing. Pick values for 'a' and 'c' tha tmake sense and adjust them to see what happens. You should be able to do this in MS Excel with reasonable accuracy.
    The thing is, I am supposed to have some background in the calculus but I am not understanding and therefore I came to this forum to presumably get some help with the task. I really do not know what I am doing and putting "random" values into the formula is not that wise, but I've tried and the results are not very pretty and thus I hope that someone can help me and show me how it can be done simultaneously...

    Sorry if I sound rude, but I am more or less desperate right now as this is only the basic function that is needed to do all the rest.
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    Quote Originally Posted by Fifi View Post
    The thing is, I am supposed to have some background in the calculus but I am not understanding and therefore I came to this forum to presumably get some help with the task. I really do not know what I am doing and putting "random" values into the formula is not that wise, but I've tried and the results are not very pretty and thus I hope that someone can help me and show me how it can be done simultaneously...

    Sorry if I sound rude, but I am more or less desperate right now as this is only the basic function that is needed to do all the rest.
    Why can't you do the following:

    1. Plot the points (use technology) to get an idea of the sort of regression model you might want to try.

    2. Use technology to do the appropriate regression.

    eg. Power regression. I get y = a \cdot x^b where a = 46.096 and b = -1.1536 and r = -0.94686.

    Why on Earth would you try doing this by hand ....?
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    Quote Originally Posted by Fifi View Post
    The thing is, I am supposed to have some background in the calculus but I am not understanding and therefore I came to this forum to presumably get some help with the task.
    Great. Did you tell us what methods you are to use? Did you suggest what section you are in? Please provide information that is helpful. Did you provide the equations you talked about? Did you show your results?

    I really do not know what I am doing and putting "random" values into the formula is not that wise, but I've tried and the results are not very pretty and thus I hope that someone can help me and show me how it can be done simultaneously...
    Who said anything about "random"? Use some sense? How many exponential equations have you seen in your lifetime? Maybe logarithmic sould be better. No one is really recommneding guessing. Use ALL the tools availalbe to you. THE MOST VALUABLE tool is your own experience.

    Sorry if I sound rude, but I am more or less desperate right now as this is only the basic function that is needed to do all the rest.
    I didn't detect any rudeness.

    I would suggest one thing. Try y = a\left(\frac{1}{x-b}\right)+c Rational function approximation is a joy.
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  11. #11
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    Quote Originally Posted by mr fantastic View Post
    Why can't you do the following:

    1. Plot the points (use technology) to get an idea of the sort of regression model you might want to try.


    2. Use technology to do the appropriate regression.


    eg. Power regression. I get y = a \cdot x^b where a = 46.096 and b = -1.1536 and r = -0.94686.

    Why on Earth would you try doing this by hand ....?
    1. I've done that, and the graph is exponential - that is why I've tried to use 1/X with different parameters but I do not know how to calculate the 'correct' parameters to use. I've attached a picture of the plotted graph, sorry for not doing it before.

    2. We do not get to use technology before we've done a fitting graph first. The instructions say "What type of function models the behaviour of the graph? Explain why you chose this function. Create an equation (a model) that fits the graph." and then "Use technology to find another function that models the data. On a new set of axes, draw your model function and the function you found using technology. Comment on any differences."

    And the results you got, are they not derived by technology? The graph seems to fit and if you haven't used technology could you then please show me how you got those results using calculations?

    Are you not supposed to be able to solve it by using simultaneous equations or any other method without using technology, or am I just supposed to guess until I get an appropriate graph?

    Thank you
    Attached Thumbnails Attached Thumbnails Graph Transformation-untitled.jpg  
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  12. #12
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    Quote Originally Posted by TKHunny View Post
    Great. Did you tell us what methods you are to use? Did you suggest what section you are in? Please provide information that is helpful. Did you provide the equations you talked about? Did you show your results?



    Who said anything about "random"? Use some sense? How many exponential equations have you seen in your lifetime? Maybe logarithmic sould be better. No one is really recommneding guessing. Use ALL the tools availalbe to you. THE MOST VALUABLE tool is your own experience.



    I didn't detect any rudeness.

    I would suggest one thing. Try y = a\left(\frac{1}{x-b}\right)+c Rational function approximation is a joy.
    We can use whatever method. I'm studying the IB diploma program and I am taking Mathematics Methods Standard leved, first year. Your equation looks yummy, but how can I find the parameters?

    Thank you

    Seriously, I'm having a very hard time finding the parameters of the function y= a(1/(x-b))+c.... can someone please, please help me... I've done some very random guessing of what these parameters may be and got f(x) = 10 / (x - 1.5) + 2.5, but still, I really have to show how I found those parameters by using calculations and I still do not believe that it is the appropriate graph I've got and... ah.... help is very appreciated, I have no, no clue at all.
    Last edited by mr fantastic; February 28th 2009 at 01:53 PM. Reason: Merged posts
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    Quote Originally Posted by Fifi View Post
    We can use whatever method. I'm studying the IB diploma program and I am taking Mathematics Methods Standard leved, first year. Your equation looks yummy, but how can I find the parameters?

    Thank you

    Seriously, I'm having a very hard time finding the parameters of the function y= a(1/(x-b))+c.... can someone please, please help me... I've done some very random guessing of what these parameters may be and got f(x) = 10 / (x - 1.5) + 2.5, but still, I really have to show how I found those parameters by using calculations and I still do not believe that it is the appropriate graph I've got and... ah.... help is very appreciated, I have no, no clue at all.
    Choose 3 points and substitute them into your model. This will give three equations in a, b and c. Solve these equations.

    Personally, I think you need to discuss with your teacher the expectation your teacher has in how you do this first part.
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  14. #14
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    Quote Originally Posted by mr fantastic View Post
    Choose 3 points and substitute them into your model. This will give three equations in a, b and c. Solve these equations.

    Personally, I think you need to discuss with your teacher the expectation your teacher has in how you do this first part.
    May you please show me an example? I don't get how I will get three equations, am I not supposed to substitute x and y? More information would help a lot more. We have not learned this http://www.mathreference.com/la-det,simeq.html yet.


    My teacher's expectations are high, but my work will be assessed by someone else outside our school and I have the right to get help with my work and discuss with other people about how to solve the task. My own knowledge about the subject, however, is very limited due to the fact of intense studying of my other subjects, which I now regret (if that is not obvious enough) and thus I really hope that I will get some further help over here...
    Last edited by Fifi; February 28th 2009 at 05:42 PM.
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  15. #15
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    Telling us methods you do NOT know really is not very helpful.

    Projects like this may take a bit of thoughtful guessing.

    Look what happens as the graph moves down the positive x-axis. Does it seem to be going somewhere? Does it level off? The answer to these questions will help you to judge a good value for "c"

    Look what happens as the graph moves up the positive y-axis. Does it seem to be going somewhere? Does it level off? The answer to these questions will help you to judge a good value for "b"

    Keep in mind that either or both could be zero (0).

    If,m in this way, you manage rational guesses for towo parameters, it shoul dnot be too difficult to find some reasonable sord of approximation for the last parameter.

    You build models by intuition.
    You solve difficult problems often by simplification.
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