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Which of the following triplets (A,g,8) are examples of functions from A to B with graph g? Mark all that apply:a.A={1,2,3},g = {(1,0),(2,0), (3,a)}, 8 = {a,b}6.A =...

Question

Which of the following triplets (A,g,8) are examples of functions from A to B with graph g? Mark all that apply:a.A={1,2,3},g = {(1,0),(2,0), (3,a)}, 8 = {a,b}6.A = {1,2,3},g = {(1,0),(2,0), (3,a)}, B = {b}cA={1,2,3},g = {(L,0), (3,0)}, B = {a,b}0dA={1,2,3},g = {(1,0),(1,b), (2,6),(3,a)}, B = {a,b}

Which of the following triplets (A,g,8) are examples of functions from A to B with graph g? Mark all that apply: a.A={1,2,3},g = {(1,0),(2,0), (3,a)}, 8 = {a,b} 6.A = {1,2,3},g = {(1,0),(2,0), (3,a)}, B = {b} cA={1,2,3},g = {(L,0), (3,0)}, B = {a,b} 0dA={1,2,3},g = {(1,0),(1,b), (2,6),(3,a)}, B = {a,b}



Answers

Which sets of ordered pairs represent functions from $A$ to $B$ ? Explain. $A=\{a, b, c\}$ and $B=\{0,1,2,3\}$ (a) $\{(a, 1),(c, 2),(c, 3),(b, 3)\}$ (b) $\{(a, 1),(b, 2),(c, 3)\}$ (c) $\{(1, a),(0, a),(2, c),(3, b)\}$

Two For the given question, that is all the given cushion. Have toe say that the given ordered Paris functional back. Let me take, for example, X camera ways are here exes, input and wise output. To say it is a function X must not be repeated on off the eggs very pitted or you can believe it. So you can see the first question here. Record the question. This is the caution. Now, from this question, I'd like to compare question from this question. Look at the X value X values here, here X values. See here X values seen here X values P If you look out here, C and C are repeated here. So it is not a function our guys a prostitution or does not the function next to her. The second question be Look at the question. Now on. Right on the question. This is the question on then at reading the question. No, Look at the cushion. Uh, X value. Look at the actual input. Yea, b c These air the x value but is not represented. No, thanks, fellas. Represents. So it is the function. Now look at this question number. See, there are Question. Look at the question. Right on the question from the question. Right on the question. Now see the X values 102 Just write the full question. By the full question, 10 to 3. See here, this is the ex. Well, it's here. 10239 of the X Well, is a reputed. So it is a function. Now look at the last question day. This is the question E had me, right? Yes. Look at the full question. Right. The full question. There is a full question. Now look at X value C B e None of the X values your repeated. So it is also a function. So there's also yeah, function.

Mhm. So for problem number 56, we're looking at two situations edition of complex numbers and they're keeping this in their abstract forms. So, no concrete values. And we're looking at the somme of complex numbers A plus B, I an a minus B. I. Compared with the graph of the difference of these two complex numbers. And hopefully we recognize that when we've got these opposite signs here. Mhm. That um these are called complex conjugate, its complex, conjugate when you change the sign of the imaginary part. So let's think back to when we are adding and subtracting complex numbers. It's almost like vectors here. So if I plot the point A plus B, I write that means I have maybe a positive real number and we're graphing this in the complex plane and a positive imaginary. So maybe here is where that point A. B. Is for that A plus B. I. What's going to change is if we have the imaginary part negative is that's gonna be the same distance A. In the real direction. But now we're going to be reflected across that real axis and we're going to be here. Okay, so let's think about this in terms of maybe some vectors, the module lists of each value there, each complex number from the origin out to that point. Now if I have um two vectors like this and I want to add them together, remember I would have to place these head to tail. So I would have to take my A. B vector. And this is gonna be our some. And what I would have to do is I would have to slide or move what the A minus B vector. I would have to move that so that its tail was at the head of the A. Plus B. I vector. So here's my A. B. Here's my A. Negative B. And remember that your resultant for this would go from the open tail toward the open head. And I think the photo for this is in picture two. So this would match the sum of our two vectors. Now. Because we can do this also algebraic lee by combining like components right? A plus A would be to A and B minus negative or B plus negative B, B minus B would give us a Vertical component zero. So that would be there are some we can work off of this first graph here where I have the two vectors tail to tail. And remember when we're subtracting vectors, we want to go from the head of the second vector and are resultant would point toward back toward the first vector. So this would represent the difference of our two vectors. So for answer choice B, we would match it with graph I in the textbook

Okay, so we're f of x ministry, and in terms of a comma, be we need to right where this would be on the line. So we've got this negative three that tells me we're going to go to the right by three units. So we're gonna add it to our x co ordinate. So this would actually end up being a plus three comma. Be because just ranges are X coordinate.

Okay, so we've got ffx minus three, and in terms of a B, we need to right where this point would be on our craft. So with this, that tells me we're going to go down for units and it's going to subtract three from our white court. So this would actually being a comma B minus three.


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