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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).$$y=-2.5 \cos \left(\frac{1}{3} \pi x+4\right)$$

## the lowest points are : $\mathrm{A}(-3.82,-2.5), \mathrm{B}(2.18,-2.5), \mathrm{C}(8.18,-2.5)$

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##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

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### Video Transcript

The question is, why is equal to negative 2.5 course sign off pi over three times X plus four. This can be rewritten as why is equal to negative 2.5 course. Sign pi over three times X plus 12 or pie. So for part, he we can analyze this equation and see that the amplitude is confined. Five. The face shift. Sorry, the A P It is, ah to pipe divided by pi over three, which is equal to six. And then the fish shift is negative 12 or pie. Now, for part B, the graph is drawn here on the right side of the screen so you can see the graph and then from the graph also, you can see that the coordinates off the minimum and the maximum point are right there. So the maximum point as approximate coordinates 5.1 here in 2.5 and the minimum point has approximate coordinates 2.18 and negative 2.4. So now let's see, what are the exact coordinates. So for partly, we start with the graph off. Why is equal to negative 2.5 course sign off high over three x So here's the graph. So we saw that the period is six off. This would be six, and this would be three, and the next maximum would be at night. So now, since we want to do, why is equal to negative 2.5 course I hi or 30 X plus 12. So what we want to do is we want to move this 12 units to the left. We're gonna move. There's 12 units to the left, and we want to move this 12 units to the left. So this first peak, of course, would become negative. So we are not interested in that. But these on a cool corners would be actually there. Wear not just moving them. 12 winners were moving them 12 over pie minutes. So the coordinates now for the minimum point would be six minus 12 over pie and negative 2.5. And the coordinates for the maximum point would be nine minus 12 your pipe and negative 2.5

Other Schools
##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University