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In X For f(J) = VJ-x State the domain and sketch this domain on the xy-plane_...

Question

In X For f(J) = VJ-x State the domain and sketch this domain on the xy-plane_

In X For f(J) = VJ-x State the domain and sketch this domain on the xy-plane_



Answers

Find and sketch the domain of the function.
$ g(x, y) = \dfrac{x - y}{x + y} $

So my equation is why is equal to forward acts? I'm looking for the domain. Well, we know that the domain is restricted by the square root because that square could not become negative. So we're only a lot of plug and X values that are greater than air equal to zero. If I graph it, it should look like this. And we do have that point at 00

That we have. Why is equal to three root X plus one? Then that means that my domain is restricted by that square root. But we do have that plus one. Which means that if we're trying to get into that this inside of this, where is zero? A greater I can have XB anything greater than or equal to negative one. Right? So then, if I want to sketch it, then I'm gonna have that point at negative one comma zero. It's gonna look like this.

48 would like us to find the demeaning to sketch the graph of the function G of X equals absolute value backs minus acts. So, Germaine of this is all real members which can also be denoted with this simple. And that is because X does not have any limitations on it. For example, there's no accident, lemaitre, or there's no X underneath the square root in order to graft this. Since this isn't a typical function, the best photograph of function like that would be to just start plotting a point. And so we can draw, are actually is was one too. And that just continues. This is one too. These continue this way and they want negative too. So we can create that teacher. I'm gonna remove us. We can create a teacher with X and X and Y values, so starting negative to know you have 1012 And in case we needed more to really get an idea of the shape we will. But for now, these should work. So when you put negative thio into jia bags, you got absolute value of negative to which is to my ass and I go to so two minus thing or two is two plus two Jia. For that you have to get 1231234 about right here and negative one obsolete by negative ones, one minus negative for So it's one plus one equals two. So they're gonna want us to about here. And 00 absolute 00 minus zero equals zero. That's right here and at one absolute value of one is one minus. One is zero absolutely of two is to minus two equals zero. And if you pay attention, that pattern is going to continue throughout the numbers to infinity. Because the use numbers the two exes will still be the same because obsolete alimony number is just itself. So it's basically like saying x minus X so you can draw a line that's like and this part of the problem is just gonna continue upwards. So another way you could have solved this forgot, And, uh, it's just probably line. But another way you could have figured out the graph with all plotting individual points would have been to solve it. Algebraic lee. So how you can do that is to split the piece wise function. Since It is an absolute value function. It will become a piece of dysfunction into two parts. So it's minus one. You can split it into two parts. You have X minus X four excess getting close zero and then you have negative X minus X ploy. Texas less than zero. And when he's single for that, you get zero for this girl. Very low zero and negatives to act for access. Listen, zero, which is what we grab. So for a number is the less than zero You have a negative two ex breath. And for numbers, grand zero, we just haven't graph where g about equal zero.

So if I have, why is equal to root X minus three? I know my domain is gonna be restricted by that square on the X so access to be greater than or equal to zero because you're not a lot of plug in anything that's negative into a square. Well, you can't have that skirt under being negative. So then for the range well, we basically took this parent function of Y is equal to rid X and moved it down by three. So instead of the range being wise, greater than or equal to zero is gonna be greater than or equal to negative three photograph. It should look something like this with this point right here is your common.


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