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Math Help - How to find possible formula for a function

  1. #1
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    Question How to find possible formula for a function




    Please help me with a). I do not understand how to find the formula from the lines.
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  2. #2
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by florx View Post



    Please help me with a). I do not understand how to find the formula from the lines.
    for g(x) you have been given two points (0,-1) and (3,0) where :

    {x_1} = 0 , {y_1} = -1, {x_2} = 3, {y_2}=0

    you can find the function using this formula:

    (y - {y_1}) = \frac{{y_2}-{y_1}}{{x_2}-{x_1}} (x-{x_1})

    Do the same for f(x)
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  3. #3
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    What would the "plain"(without the 1 or 2 next to it) x and y be in the formula (y - y1) = (y2-y1)/(x2-x1)*(x-x1)?
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    MHF Contributor harish21's Avatar
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    Quote Originally Posted by florx View Post
    What would the "plain"(without the 1 or 2 next to it) x and y be in the formula (y - y1) = (y2-y1)/(x2-x1)*(x-x1)?
    for g(x), your function will be:

    y-(-1) = \frac{0-(-1)}{3-0} (x-0)

    y+1 = \frac{1}{3} x

    y = \frac{x}{3} -1

    \therefore g(x) =  \frac{x}{3} -1 = \frac{x-3}{3}

    As instructed before, do the same for f(x).

    Remember that you are using two-point form to find the equation(s) of the line(s).

    Linear equation - Wikipedia, the free encyclopedia
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  5. #5
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    Thank you so much for your continual help. I got the same answer using the
    y = mx + b method.

    Anyways should there be a limit on what x values these formulas should operate in? Because if there wasn't any, the lines will proceed to go further than the point of intersection between f(x) and g(x).
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  6. #6
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by florx View Post
    Thank you so much for your continual help. I got the same answer using the
    y = mx + b method.

    Anyways should there be a limit on what x values these formulas should operate in? Because if there wasn't any, the lines will proceed to go further than the point of intersection between f(x) and g(x).
    Yes, the lines will go further beyond their point of intersection. The picture just shows a small portion of those two lines. Look at the graph given in the Wikipedia link.
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