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Math Help - How to find f(x) by just a graph?

  1. #1
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    How to find f(x) by just a graph?

    My question is on here : SparkNotes: SAT Subject Test: Math Level 2: Review Questions

    #5. I don't get why and I don't get its explanations

    Sorry for just pasting the website, I cannot copy the diagram. Thanks in advance!!
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  2. #2
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    Hello, fabxx!

    I don't get its explanations either . . .


    5. A portion of the graph of y = f(x) is shown.
    Code:
                     |
         *           | *
                     *   *              *
          *          |    *
           *        *|                 *
      - - - -*- - -*-+- - -*- - - - - * - - -
                *    |       *      *
                     |           *
                     |

    Which of the following could be f(x) ?

    Note that the graph has four x-intercepts, two positive and two negative.



    (A)\;x^4 + ax^3 + bx^2 + cx .No
    One of the x-intercepts is 0; this graph would contain the origin.


    (C)\;-x^4+ax^3 + bx^2 + cx + d .No
    This quartic opens down.


    (D)\;x^3 + ax^2 + bx + c .No
    This is a cubic function.


    (E)\;x^4+b^2x^2+c^2 .No
    To find the x-intercepts: . x^4 + b^2x + c^2 \:=\:0

    Quadratic Formula: . x^2 \;=\;\frac{-b^2 \pm\sqrt{b^4-4c^2}}{2}

    It can be shown that the right side is either negative or zero.

    . . If it is negative, there are no real values of x.

    . . If it is zero, there is only one x-intercept.



    (B)\;x^4+ax^2+b .Yes

    To find the x-intercepts: . x^4 + ax^2 + b \:=\:0

    Quadratic Formula: . x^2 \;=\;\frac{-a \pm\sqrt{a^2-4b}}{2}

    If a is negative, the right side is positive.


    Hence, for a < 0, there are four x-intercepts:

    . . x \;=\;\pm\sqrt{\frac{-a \pm\sqrt{a^2-4n}}{2}}

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  3. #3
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    But the function in B is an even function while the graph is not that of an even function. So as written there is no answer.

    Look at question #6. The given graph is not an odd function either.

    That is just a poor set of problems and they are selling them as SAT review.
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  4. #4
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    HAHAH thanks for reply Soroban. And also Plato!! haha
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