Question

Match transformation of the function y = csc x with description of the resultant shift in the original cosecant graph. Tiles -1 + csc(x − π) -1 + csc(x + π) 1 + csc(x + π) 1 + csc(x − π) Pairs Resultant Shift in the Function's Graph Transformation of the Function The graph of csc x shifts one unit down and π radians to the left. arrowBoth The graph of csc x shifts one unit up and π radians to the right. arrowBoth The graph of csc x shifts one unit down and π radians to the right. arrowBoth The graph of csc x shifts one unit up and π radians to the left. arrowBoth

Answer 1

We are given with the original trigonometric function
y = csc x
We are also given different transformations of the original trigonometric function
-1 + csc(x − π)
-1 + csc(x + π)
1 + csc(x + π)
1 + csc(x − π)
An addition or subtraction in the domain will result to a vertical shift. If there is a 1 added to the function, the shift will be one unit upward and if there is a -1 added, the shift will be one unit downward.
In the argument of the cosecant function, addition or subtraction results to a horizontal shift. The addition of π will result to a shift of π radians to the left and subtraction will result to shift in the opposite direction.
So, the answer are:
-1 + csc(x − π) - The graph of csc x shifts one unit down and π radians to the right
-1 + csc(x + π) - The graph of csc x shifts one unit down and π radians to the left
1 + csc(x + π) - The graph of csc x shifts one unit up and π radians to the left
1 + csc(x − π) - The graph of csc x shifts one unit up and π radians to the right