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The function f(k) belaw:cos(bz) + cis plotted on the graph shownWhat are the values of a=and...

Question

The function f(k) belaw:cos(bz) + cis plotted on the graph shownWhat are the values of a=and

The function f(k) belaw: cos(bz) + cis plotted on the graph shown What are the values of a= and



Answers

Find $a, b,$ and $c$ for the function $f(x)=a \sin (b x-c)$ such that the graph of $f$ matches the graph shown.

If X is equal toe a sign off BX minus e me to find out the value off a B and C. Now, if you see in the graph, fo zero is equal to zero. So this implies there is no shifting in the graph. Therefore, Devalue C is so this implies that season or does it now? If you see f off zero plus means we are going in the positive direction to zero, it is greater than zero, so this implies that is greater than zero. We have not exactly calculator, but we know that they will be on base positive. Now. Can we find out the Maximilian the minimum value of the graph so maximum value is to on the minimum value is minus true, We have been given the maximally as to and minimally as to minus two. Therefore, we can say that it would be equal to plus two because from here, before that is positive on here, we can see that the amplitude is too since is positive and the opportunities to a comes out to be plus to know. Let's talk about being so. The graph completes the graph completes, completes one cycle in is in order to vices the Jarvis completing only one cycle inserted by therefore the value of becomes out to be one. So we can write effects is equal to a that is plus to sign off X and C zero. So this will be the function if it is going to sign x.

If X is equal, do a sign off BX minus you to find out the value off a B and C If you see the graph, the graph repeats exactly one invulnerable by. So the graph the pizza You can see the graph completes one cycle in zero. Close the door to Dubai. So since the graph is completely only one cycle, therefore B is equal to one. So we got the value of B. Now we know the maximum value. The maximum value is one on the minimal value is minus one. Since the maximum value is one of the men who values minus one, this implies that it would be equal to one. So we got a we got to be. Now if you see closely and the graph you can find out that f off the graph is having won the value fun in between the middle point off Bye bye to on by So the water the midpoint off by by two and five. So it would be weird to 354 So at three pie by four, the graph is coming up will be one. So if we after dying this FX, we can say that if off three by by four is equal to one which is equal Do if it's a subsidy value off the envy. So this sign off X minus c So can we saw this equation to give the value of seeing very, very weak and easily sold. So if you take the signing was bored. Side we get by by two is equal to X minus e What is the value? Off exit Just by by four. So this implies that bye bye to minus 35 by four is equal to see. This implies that Sesay will go. Bye bye food. So we got devalue off effects effects is equal. Do it. That is one So decide off be It is one so x minus by by four. So this is gonna buy you off if X

You have been given that effects is equal toe a sign off the X minus C. Now, if you see, look at the graph graph is repeating exactly 1.5 times so you can save 1.5 times in zero to go by. So the graph complete 1.5 cycle in their photo by. Since the graph is completing violent, 1/2 cycle is they don't want to buy. This implies that B is equal to three by two. So we got the value of be no next. Find out, devalue off if you see the maximum value of the half, so maximum value is equal. Do plus two on the minimum value off the graph is equal to minus two. This implies that it would be equal to tow the Aboriginal people do toe because it is the maximum distance off Maxim point or the point from the mean position. So what we get, we get f off X is equal to go. Who sign off Beastie by two x minus e. No, me to find out. See if you see the grab that F of zero has given us toe. So let's substitute zero where your and get the value of C. So who is equal toe to sign off? Yes. Observing 00 minus. Is this to end us to gets cancer, We get sign off minus C is equal to one. This implies that minus C is equal to sign in worse one on what a sign was going to spy by go So this implies that season could do minus bye bye to So you can see that if X is equal to advice Off Sign off three by two X We have kept minus e So it is minus off minus five. I do. It will be giving you clasp. I do so this will be the value off effects for this. The given graph in the question.

Okay, we are given a graph when we are asked to come up with an equation. So it's interesting when doing sine and Cosine equations because you can often come up with multiple answers, fortunately they've asked us to center in on sign and didn't give us a choice between sign and co sign because that would have been a hard decision. So because we're sign, we can first look at our amplitude really with anything. We first looked at our amplitude. So we see that we have that amplitude of three, but we also notice that it's a flipped sign graph. So we could do a shift of um negative pi over two or pi over two, but would be easier to just do a flipped sign here. Now the period for one rotation goes between zero and pi. So remember to pi over B was our period. So we can actually solve for R. B by using that same equation. Okay, so now we are going to look at actually the phase shift now, remember um see um over B is our phase shift, but we really have no phase shift here because we're actually starting where we want to start right at zero. And so we also don't have any sort of vertical shift. Um but they don't even give us the opportunity to find a devalue. So now that we've kind of found some of our pieces, we found our A. R. B. And that R. C. Is zero, we can go ahead and write our function. So f of x equals negative three sign of two X. And then just the check that um when I see that too, I know that two periods should happen between zero and two pi and I actually see that happening, so I'm happy with our answer.


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