# Investigation Transformations.

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. The minimum is the negative of the a value, so therefore in y = 2sin(x), -2 would be the minimum.

Investigation # 2

These transformations were of cos graphs. In this investigation the k value of the equations were changed. As shown when the k value is greater 1 the graph is compressed horizontally by the factor 1/k as seen in y = cos(2x). When the value of k is greater than 0 but less than 1 like in y = cos(1/2) the graph is stretched horizontally by a factor of 1/k. As you can see all the graphs pass through the y-axis at 1 but the graphs do not pass through the x-axis at the ...