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Problem 68

Graphical Reasoning In Exercises 67 and $68,$ find $a, b,$ and $c$ such that the graph of the function matches the graph in the figure.

$$y=a \sin (b x-c)$$

Answer

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## Discussion

## Video Transcript

find A that the graph of the function matches the graph in the figure. Why Apple's a sign it be eggs Menace E. Now I think the easiest place to would be to begin read by looking at the amplitude. And so remember that the that distance between the center line of our graph and its maximum of imam points. So if we look here, we see the NUM, both sides that's equal to 1/2 so we can safely say a equals 1/2 suite where 1/3 of the way done. Now let's look at the period of our graph photograph goes through one full revolution or fall oscillation from zero off now normally. But now the period is pie and we can do some. If I what that be value is period is equal to two pi divided might be. We know that the period now is equal to pi. So be it equals to pie Divide of my pie Cancel a pi equals two Great, So be equals two. And now this see value is going to correspond to the shift of our graph along, um, this horizontal axis Now normally our graph has an upward positive sloping intercept at zero. But we can see that there's a negative downward intercepted zero, which means it's been shifted over this distance right here. Pi house. Now, to shift our graph to the right, we end up subtracting that amount. So see is going to equal High House because it has been shifted to the right by that mountain. So you would do minus my house. All right. And there you have it. A, B and C have been found.

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