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# (a) Using pencil and paper, not a graphing utility, determine the amplitude, period, and (where appropriate) phase shift for each function.(b) Use a graphing utility to graph each function for two complete cycles. [In choosing an appropriate viewing rectangle, you will need to use the information obtained in part (a).](c) Use the graphing utility to estimate the coordinates of the highest and the lowest points on the graph.(d) Use the information obtained in part (a) to specify the exact values for the coordinates that you estimated in part (c).$$y=-2.5 \cos (3 \pi x+4)$$

## the lowest points are : (-0.42,-2.5),(0.24,-2.5),(0.91,-2.5)

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### Video Transcript

we have the equation. Why is equal to negative 2.5 course sign off three High X Plus four, which can be rewritten as why is equal to negative 1.5 co signed the Pi Times X plus four over the place. So for part A, we can look at the equation and see that the amplitude is 2.5. Also, the period is two pi divided by three pie, and that's equal to 2/3. And then the phase shift these negative for over three pie. For Part B, you can see the draft on the right side of the screen and for part C as well. You can look at the graph and you can see that the coordinates of the maximum point car approximately 0.0.5756 and 2.5 and the accordance off a minimal point are approximately point to 4 to 3 and negative 2.5 Now for Partney. We want to find the exact values off these coordinates, so let's take a dig in for party. So we have. We'll start with the quick graph for Y is equal to negative 2.5 course sign off three Pi X. So what this craft will look like is something like this. So this would be 1/3, and this would be to orthe e because we just said that opinion is to over three. And then the next peak would be at what now, for why is equal to me that it pence off or why is equal to negative 2.5 course sign three high X plus 4/3 pipe. What we need to do is we need to shift these points to the left by an amount equal do for over three pipes. So this first maximum is actually gonna become negative, and this minimum is going to become somewhere to over three, minus four or three pie. And this is going to become one minus four or three pie. So now we can write the corners off the minimum point and the corners off. The minimum point would be to over three minus 4/3 pie and a negative complete five and the corners of the maximum point What I eat one minus four were three pipe and two point fight

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