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Math Help - Polynomial Functions

  1. #1
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    Polynomial Functions

    Hey all,

    I just had few questions that couldn't wait until I see my teacher to clear up. Hopefully someone won't mind explaining...

    1. I've never encountered the symbol "|", as in (x | 2) . What does it mean, and how would I go about deciding it's use?

    2. What role does 'K' play in the equation f(x) = k(x - s)(x - t)(x - u)etc.?
    I know that if k is negative, we reflect the graph in the x-axis, but is it also (as I remember it) the term that will stretch the graph vertically?

    3. An application question gives me a function y = 26.55x^3 - 170.56x^2 + 249.62x + 1257.80, 0 < x < 4 and asks me to state the restricted domain... I'm not sure if it *is* 0 < x < 4, or what. It's just a guess, and I need an explanation really.

    Thanks to anyone who takes the time to give me hand yet again!

    - Cam
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  2. #2
    Moo
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    Quote Originally Posted by Cam5 View Post
    Hey all,

    I just had few questions that couldn't wait until I see my teacher to clear up. Hopefully someone won't mind explaining...
    Of course ^^
    1. I've never encountered the symbol "|", as in (x | 2) . What does it mean, and how would I go about deciding it's use?
    It depends... Is "x divides 2" appropriate for you ?

    2. What role does 'K' play in the equation f(x) = k(x - s)(x - t)(x - u)etc.?
    I know that if k is negative, we reflect the graph in the x-axis, but is it also (as I remember it) the term that will stretch the graph vertically?
    Yes, sort of. Imagine f(x) represents the y-ordinate of any point. If you increase k, it means you increase f(x), that is to say for each point, you increase the y-ordinate. So it looks like you're stretching (or narrowing if you make k decrease) the curve.

    3. An application question gives me a function y = 26.55x^3 - 170.56x^2 + 249.62x + 1257.80, 0 < x < 4 and asks me to state the restricted domain... I'm not sure if it *is* 0 < x < 4, or what. It's just a guess, and I need an explanation really.
    Yes it is. You're told that this equation holds for 0<x<4. Thus it can be considered as the domain.
    If you want an example of an application... hmmm let's see.

    You can define a function as being :
    f(x)=\left\{\begin{array}{lll} 1257.8 \quad \text{ if $x \leq 0$} \\ -170.56x^2 + 249.62x + 1257.80 \quad \text{ if $0<x<4$}\\ 1336.86 \quad \text{ if $x \geq 4$} \end{array}\right.

    It means it takes these values if x is in the given domains.
    In that case, the restricted domain of -170.56x^2 + 249.62x + 1257.80 is (0;4)


    I hope it looks clear... If not, just ask.
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  3. #3
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    Moo, you're always very helpful and prompt! Sorry for the delay in reply.
    Thanks for taking the time once again to teach me something.

    As is your style - I got more info than I bargained for - my questions were clarified, and I did end up solving my problems with a little more confidence and background info.

    Cheers,

    - Cam
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