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Precalc

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how do I graph this function?

x^2-xy+2x-1=0

  • Precalc - ,

    x ^ 2 - x y + 2 x - 1 = 0 Add xy to both sides

    x ^ 2 - x y + 2 x - 1 + x y = 0 + x y

    x ^ 2 + 2 x - 1 = x y

    Roots :

    When y = 0 then :

    x ^ 2 + 2 x - 1 = x * 0

    x ^ 2 + 2 x - 1 = 0 Add 2 to both sides

    x ^ 2 + 2 x - 1 + 2 = 0 + 2

    x ^ 2 + 2 x + 1 = 2

    ________________________________________

    Remark :

    x ^ 2 + 2 x + 1 = ( x + 1 ) ^ 2

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    ( x + 1 ) ^ 2 = 2 Take the square root of both sides

    x + 1 = + OR - sqrt ( 2 ) Subtract 1 to both sides

    x + 1 - 1 = + OR - sqrt ( 2 ) - 1

    x = + OR - sqrt ( 2 ) - 1


    x1 = sqrt ( 2 ) - 1 = approx 0.41

    x2 = - sqrt ( 2 ) - 1 = approx. - 2.41



    Revrite x ^ 2 + 2 x - 1 = x y

    Divide both sides by x

    x ^ 2 / x + 2 x / x - 1 / x = x y / x

    x + 2 - 1 / x = y

    y = x - 1 / x + 2


    for x = 0

    x - 1 / x + 2 -> + OR - infinity


    Go on wolfram alpha dot com

    When page be open in rectangle type :

    plot x ^ 2 - x y + 2 x - 1 = 0

    and click option =

    You will see graph

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