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Thread: Functions

  1. #1
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    Exclamation Functions

    Hey guys, I have a big test coming up and I need to know how to do these problems. So thanks if you can help or even taking the time to look at them.

    Given the function f(x) = x^(3) - 3x^(2) + 2x

    (A) find the real roots (x-intercepts)

    (B) what is the y-intercept
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  2. #2
    MHF Contributor red_dog's Avatar
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    To find the x-intercept you must solve the equation $\displaystyle f(x)=0$.
    Then $\displaystyle x^3-3x^2+2x=0\Leftrightarrow x(x-1)(x-2)=0$

    To find the y-intercept you have to calculate $\displaystyle f(0)$
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  3. #3
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    sorry im still confuse
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  4. #4
    MHF Contributor red_dog's Avatar
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    $\displaystyle x(x-1)(x-2)=0\Rightarrow x_1=0, \ x_2=1, \ x_3=2$
    So, the x-intercepts are $\displaystyle O(0,0), \ A(1,0), \ B(2,0)$

    $\displaystyle f(0)=0$, so the y-intercept is $\displaystyle O(0,0)$
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  5. #5
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    Quote Originally Posted by uniquereason81 View Post
    sorry im still confuse
    What are you confused about??
    Do you understand how the factorised form $\displaystyle x(x-1)(x-2)$ of f(x) is got?
    Do you know how to solve the equation $\displaystyle x(x-1)(x-2)=0$?
    Do you know what calculate f(0) means? Do you know why you have to calculate it?

    There's not a lot to get confused over ...... How much work have you actually done in preparing for the big test?
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  6. #6
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    so you unfoil the eaquation , set it to zero
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  7. #7
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    i just don't want to over look anything
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