# Thread: Converting an equation in one variable to a function

1. ## 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?

2. ## Re: Converting an equation in one variable to a function Originally Posted by B9766 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