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Investigation Transformations.

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Introduction

Investigation Transformations. Part B: Investigation # 1 These transformations were of sin graphs. When the a value in y = a sin k (x-b) + d is positive the transformation is vertical and the graphs are stretched or compressed by a factor of a. When a is negative the transformation is inverted or reflected and stretched or compressed vertically by a as seen in y = -3sin(x). The period of all these graphs remains the same and all graphs intersect the origin and intersect the x axis at the same points. The maximums of these graphs are the numbers are the positive of the a values. So in y = 2sin(x), the maximum is 2. ...read more.

Middle

From these graphs we can determine that the value of k determines the number of cycles in the period of the graph. As seen in the following graph the k value was increased to 3 and it is shown that the more than one cycles appears in the period. Investigation # 3 These transformations were of tan graphs and the b values were changed. From the graphs we can determine that when b is than 0 the graph is horizontally shifted b units to the left. When b is less than 0 the graph is horizontally shifted b units to the right. The b value is called the phase shift because it causes horizontal translations. ...read more.

Conclusion

If the k is changed in the graph the graph is compressed or stretched horizontally. If k is greater than 1 the graph is compressed by a factor of 1/k, if k is less than 1 but greater than 0 then the graph is stretched by a factor of 1/k. When the b value is changed the graph is shifted horizontally left and right. So when b is greater than 0 the graph shifts b units to the left and if b is less than 0 the graph is shifted b units to the right. Finally if the d value is changed the graph is shifted vertically up and down. If d is greater than 0 the graph shifts d units up and if d is less than 0 the graph is shift d units down. ...read more.

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