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    • Thread Starter

    Hello guys, I'm stuck on this question part iv and I don't understand what to do. I know that its a translation of (1 3) from the equation (y=1/x). I substituted 1/x into the equation and translated it but it got me nowhere.


    What have you substituted 1/x into?

    For a general equation f(x), f(x-a) is a translation of a to the right and f(x) + a is a translation of a upwards.
    So just use those to get an equation for the translated graph, then you can re-write that equation in the form they want and get the values for a, b, c.
    • Thread Starter


    This is what I got when I substituted (1/x)

    (Original post by medrawr)

    This is what I got when I substituted (1/x)
    You don't need to subsitute 1/x into the (ax-b)/(x-c), that is just a form of equation like 1/(x-d) + e is another form of equation.
    For example: you can write (x+1)^2 in the form (x^2 + 2nx + m). Expanding (x+1)^2 = x^2 + 2x + 1, so n=1 and m=1 are the values n, m, for which (x^2 + 2nx + m) is the square of (x+1).

    If the equation was y = g(x), where g just stands for a function, then y=g(x-1) +3 would be g(x) transposed by (1 3). In this case your function g(x) is 1/x, so the transposed function would be 1/(x-1) + 3

    You can then rewrite this in a different form- since 3 = 3(x-1)/(x-1), the equation

    y = 1/(x-1) + 3 y= 1/x transposed by (1 3)

    is equivalent to:

    y = 1/(x-1) + 3(x-1)/(x-1)

    which is equivalent to:

    y = (1 + 3x - 3)/(x-1)


    y = (3x -2)/(x-1)

    Now compare this to the form they wanted:

    y = (ax-b)/(x-c)

    What values do you substitute for a, b, and c to get your transposed equation? Those will be the values a, b, c for which f(x) = (ax-b)/(x-c) is a transposition of (1 3) of f(x).
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Updated: October 29, 2015
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