find equation of cosecant graph

In this math example, we are given the graph of a function and asked to find the equation of the function that will produce the graph. To do so, we first determine if we want to utilize the secant sec(x) or cosecant csc(x) graph. For this example, we initially choose the cosecant graph based on the location of vertical asymptotes. Then we find each value to create the graph based on values from the y-axis and the period of the graph. We also find the equation of the secant function that would produce the same graph but it requires some extra effort as that graph would also have a horizontal transformation when compared to using the cosecant function.