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Thread: Problems with functions...

  1. #1 Problems with functions... 
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    Hi everyone. I searched the internet for a nice website, which explains the functions nicely. I was unable to find any good site, as most of the sites explains very advanced or very simple functions. Like... f(x)=bx or f(x)=bx^2. Or logarytmic functions. I don't need logarytmic functions, I need functions something like these: f(x)=ax+bx-c. For example: Find the range of: f(x)=-x^2+5x-6. Or:
    y=ax^2+bx fraph goes trough points: (-1;1),(2;10). I need to find what is the a and b. Or calculate something like this: [5,8]+[-5,8]. Or... f(x)=4x-5 and I need to find a... vice versa function. Then graphs drawing... And... compare f(x)=x^6 and x^7, if f(3.5) and f(-4.2).

    Those were examples of the exercises I have to do. Actually a) variant of each exercise, they have variants up until f or g sometimes. I don't have to do them as homework, but I'm having a test on Monday, and I'd like to get ready for it.

    Hope you can help me out with this, thanks.


    Sorry for my poor English skills, I've learned it by myself... Trying to improve them, feel free to criticize, hehe.
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  3. #2 Re: Problems with functions... 
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    Quote Originally Posted by geekish
    Hi everyone. I searched the internet for a nice website, which explains the functions nicely. I was unable to find any good site, as most of the sites explains very advanced or very simple functions. Like... f(x)=bx or f(x)=bx^2. Or logarytmic functions. I don't need logarytmic functions, I need functions something like these: f(x)=ax+bx-c. For example: Find the range of: f(x)=-x^2+5x-6. Or:
    y=ax^2+bx fraph goes trough points: (-1;1),(2;10). I need to find what is the a and b. Or calculate something like this: [5,8]+[-5,8]. Or... f(x)=4x-5 and I need to find a... vice versa function. Then graphs drawing... And... compare f(x)=x^6 and x^7, if f(3.5) and f(-4.2).

    Those were examples of the exercises I have to do. Actually a) variant of each exercise, they have variants up until f or g sometimes. I don't have to do them as homework, but I'm having a test on Monday, and I'd like to get ready for it.

    Hope you can help me out with this, thanks.
    It seems that you are studying quadratic functions; these are functions of the second-order. For your purposes at the moment this page should suffice: http://en.wikipedia.org/wiki/Quadratic_function


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  4. #3  
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    Sorry to say that, but it didn't helped much. Thanks though.
    Sorry for my poor English skills, I've learned it by myself... Trying to improve them, feel free to criticize, hehe.
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  5. #4  
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    Quote Originally Posted by geekish
    Sorry to say that, but it didn't helped much. Thanks though.
    Well if you need help with any specific problems feel free to post them and I will help you work them out.
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  6. #5  
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    Okay, well... To get the concept, I would like to ask help with this exercise:
    f(x)=-x^2+5x-6. I need to find the range of it. I know the answer from the book, but I don't know how to get that answer.

    And one more from the... 'hot' ones:
    f(x)=(x^2-1)/(x+1). I need to find with which numbers f(x)=0.

    Figured how to draw graphs and how to find if it's even odd or neither somewhere.
    Sorry for my poor English skills, I've learned it by myself... Trying to improve them, feel free to criticize, hehe.
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  7. #6  
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    Well the range is all possible y-values of that function. First, you have to determine whether the function has a maximum or a minimum. Because a is negative here, we know that this function is concave down, i.e., it has a maximum. A quadratic equation cannot have a maximum and a minimum. We also know that, for any quadratic equation, , is the x-coordinate of the vertex. What this means is that the coordinates of the vertex of a parabola are . In thise case, they would be . Now the parabola's range extends to all y-values at or below the minimum, because it is continuous, (now if we had a minimum it would be all y-values at or above the minimum). So we could say that .

    For your second problem, you simply need to recall the formula . So .

    If you would like me to help you with more problems, such as proofs for the formulas or if you have more examples, feel free to write again.
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  8. #7  
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    Thanks, that helped me do one of the exercises given in the test. Don't know if I did it right though.

    Anyway, I don't have questions now, as I'm waiting for the mark and mistakes, but I will have some later. Maybe I could PM you with them, or you prefer, that I'd post them here?
    Sorry for my poor English skills, I've learned it by myself... Trying to improve them, feel free to criticize, hehe.
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  9. #8  
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    Whatever you'd prefer.
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  10. #9  
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    Well, since you haven't written back, than I will prove the aforementioned formulas now (in case any other young members were keeping up with this post, as I'm aware young, mathematical minds often need more than answers: they need reasons).

    For all , . We therefore have than that the critical value of the derivative of a quadratic to be the x-coordinate of its vertex:







    Now, we can simply plug in the derived formula for x into the definition of a quadratic to find the y-value of its vertex:













    Therefore, we have the coordinates of the vertex of any parabola, , to be the following:



    Now for the formula :









    QED

    If anybody has any questions feel free to ask.
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