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Identify Symmetry In Cosecant Graphs

Complete:

The graph of csc(x)\csc\left(x\right) is not symmetric about the __________.

Is the sentence true or false?

The cosecant graph has no x-intercepts.

Complete:

The graph of csc(x)\csc\left(x\right) is symmetric about the __________.

Is the sentence true or false?

The graph of cscx\csc x is symmetric about the y-axis.

Is the sentence true or false? 

the graph of y=secxy=\sec x is symmetrical about the vertical line y=3y=3.

Is the sentence true or false?

The extended csc\csc graph has reflection symmetry about any multiple of π.

Is the sentence true or false?

The extended csc\csc graph has a translation symmetry by 2π.

Is the sentence true or false?

the graph of y=cscxy=\csc x is symmetrical about the vertical line x=πx=\pi.

Is the sentence true or false?

The extended csc\csc graph has a rotational symmetry about any even multiple of π2\frac{\pi}{2}.

Is the sentence true or false?

The graph of the function 2+csc(x)2+\csc\left(x\right) is symmetric about the y-axis.