Is the equation y 2 + 2 x = 10 y^2+2x=10 y 2 + 2 x = 10 a function? If so, rewrite it in function notation and evaluate at f ( − 1 ) f\left(-1\right) f ( − 1 ) .

Welcome back, everyone. So let's give this problem a try. In this problem, we have the equation y squared plus 2x equals 10. We want to determine whether or not this is a function, And if it is a function, we want to rewrite it using function notation and evaluate it at f of negative one. So what I'm first going to do here is see if there is anything familiar from this equation that will give me any kind of hint here. And looking at this, notice we have y raised to an even power. Whenever y is raised to an even power in these types of equations, that means that you do not have a function. So we can say for this situation that this is not a function. Now if you did not remember this rule or there was or these steps, didn't seem clear, there is another thing that you can do. But the process takes a little bit longer. So what you wanna do is take your equation and you want to solve for y. So in this case, what I'll do is subtract 2 x on both sides of the equation to cancel the 2 x right there, giving me that y squared is equal to, 10 minuteus 2 x. Now from here, we can take the square root on both sides of the equation to cancel the square on the y, giving me that y is equal to plus or minus the square root of 10 minuteus 2x. And for this situation, you're going to have a plus or minus whenever you take the square root on both sides. Now what I can do is try some various values for x to see if we ever get multiple solutions for y. So we see we could try 0 or negative one or positive one, and if we ever see that one x gives us multiple y's, we know that the equation is not a function. So what I'm gonna do is try 0 because I think that's a pretty simple one. So we have y is equal to plus or minus 10 minuteus 2 times 0. In this case, the 2 times 0 is just gonna be 0, so all we're going to end up with is that y is equal to plus or minus the square root of 10. But notice in this situation, we're going to end up with a positive square root of 10 and a negative square root of 10 because we could write this as plus square root 10 and minus square root 10. And because we can see that we're going to get 2 different answers for y, for one x would give us multiple y's, we can already tell that this is not a function. So this is the way that you could do it if you did not immediately recognize that y is raised to an even power. Now since we verify that this is not an example of a function here, then that means that we do not need to evaluate this at negative one, because we already figured out that it's not a function, so we do not need to do the rewriting in function notation. So that is the solution to this problem. Hopefully, this video helped you out.