Determine whether each equation defines y as a function of x. 2x ...

Question

Determine whether each equation defines y as a function of x. 2x + y^2 = 6

Accepted Answer

Hello today we're going to solve an equation and determine whether that equation is a function or not. So the equation given to us is x squared plus y minus one is equal to zero. Now we want to rewrite this into the form of a function that means that we're gonna want to go ahead and solve for why. In order to start that process, I'm gonna first go ahead and add one to both sides of this equation. Doing so is gonna leave me with X squared plus y is equal to one. Now I want to go ahead and get y by itself. So I'm gonna go ahead and subtract X squared to both sides of this equation. Doing so is gonna leave me with Y is equal to negative X squared plus one. So our equation is now in the form of a function. Now we need to figure out is it a function. And in order to determine whether it's a function or not, we can go ahead and use the vertical line test. Now in order to use the vertical line test we need to first graph this function. So let's go ahead and do that. Well what kind of graph is this? Well since the exponent of the graph is squared, that means that this graph is going to be a parabola and this is gonna be a parabola what the origin at zero comma one because of the positive one here. And since this has a leading negative, this is going to be a negative parabola. So now we have the shape of our graph. And in order to perform the vertical line test, we're just gonna go ahead and draw vertical lines throughout this graph. Now, if you notice every vertical line that I'm drawing intersects the graph at exactly one point at any given location, that means that this is a 1-1 function, which confirms that yes this is a function and that is gonna be the solution to our problem. So it's a function and the answer is a. So I hope this video helps you into solving equations and determining whether that equation is a function and I'll go ahead and see you all in the next video.

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