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Thread: Converting an equation in one variable to a function

  1. #1
    Junior Member B9766's Avatar
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    Converting an equation in one variable to a function

    This is probably a really stupid question but it's been bugging me.

    The problem in the textbook says: "Use a graphing utility to approximate the solutions to the equation $x\ =\ 2sin(x)$ on the interval [$-\pi,\ \pi$].

    It then says: "Begin by graphing the function $y\ =\ x-2sin(x)$".

    I would have tried to graph $y\ =\ 2sin(x)-x$ by subtracting x from both sides of the original equation. Why did it convert from the equation to the function the opposite way? The solutions for x come out the same either way but the y values are mirrors (inverses) between the two functions. If I had to submit the graph as part of the answer, would it be wrong? Am I trying to make this too complex?
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    Forum Admin topsquark's Avatar
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    Re: Converting an equation in one variable to a function

    Quote Originally Posted by B9766 View Post
    This is probably a really stupid question but it's been bugging me.

    The problem in the textbook says: "Use a graphing utility to approximate the solutions to the equation $x\ =\ 2sin(x)$ on the interval [$-\pi,\ \pi$].

    It then says: "Begin by graphing the function $y\ =\ x-2sin(x)$".

    I would have tried to graph $y\ =\ 2sin(x)-x$ by subtracting x from both sides of the original equation. Why did it convert from the equation to the function the opposite way? The solutions for x come out the same either way but the y values are mirrors (inverses) between the two functions. If I had to submit the graph as part of the answer, would it be wrong? Am I trying to make this too complex?
    You are fine. The solutions to x = 2 sin(x) will be where the function y = 2 sin(x) - x = 0. These are the same x values for y = x - 2 sin(x) = 0.

    -Dan
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