In Exercises 11–26, determine whether each equation defines y as ...

Question

In Exercises 11–26, determine whether each equation defines y as a function of x. x + y = 16

Accepted Answer

Welcome back. I'm so glad you're here. We have the equation X minus Y equals 39 we are to determine if it defines Y as a function of X. And so in order to do that first, we want to get why by itself on one side of the equation. So let's subtract X from both sides. So now we have a negative Y equals minus X. And let's divide both sides by a negative one. So we'll have Y equals will have a negative 39 plus X. Or we could rewrite that as Y equals X minus 39. Alright. We've got why by itself on one side and now the question to ask ourselves is for every value of X, is there one value of why? And yeah, for any number we could put in for X. We'd get one value of for why as our solution and a really good clue to know whether this is the case is that we don't have a plus or minus on the right hand side of the equation. We didn't take the square root of why anywhere and end up with a plus or minus over toward our X. So in this case There is only one value of Y for every value of X and therefore why is defined as a function of X. We look at our answer choices and that matches with answer choice. A well done, we'll catch you on the next one

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In Exercises 11–26, determine whether each equation defines y as a function of x. x + y = 16