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We have to select all of the transformations that could change the location of the asymptotes of a cosecant of secant function.
So given function can be written as:
y=csc( sec(x))
First we need to determine the location of asymptote which is basically a line that seems to be touching the graph of function at infinity.
From attached graph we see that Asymptotes (Green lines) are vertical.
So Vertical shift or vertical stretch will not affect the location of asymptote because moving up or down the vertical line will not change the position of any vertical line.
only Left or right side movement will change the position of vertical asymptote. Which is possible in Phase shift and period change.
Hence Phase shift and Period change are the correct choices.
