SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given range
[tex](-\infty,-9\rbrack\cup\lbrack5,\infty)[/tex]
STEP 2: Find the cosecant function
[tex]\begin{gathered} \text{The range of a cosecant function normally excludes the interval }(-1,1)\text{.} \\ The\text{ range in the question excludes the interval }(-9,5)\text{, which has a width 7 times as great.} \\ \text{Thus, we know the vertical factor is 7.} \\ \\ T\text{he midpoint of the excluded interval of the given function is }\frac{(-9+5)}{2}=-\frac{4}{2}=-2 \\ so\text{ that is the vertical translation.} \\ \text{The cosecant function normally has vertical asymptotes at }x=0\text{ and }x=\pi\text{ so the function is } \\ \text{expanded horizontally by a factor of }2. \end{gathered}[/tex]
Hence, the cosecant function is
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