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It's difficult for me to be sure what function you are asking about, because of the limitations of answers.com.
I am considering y = -1 + csc (x)
csc (x) = 1/sin(x) and sin is a periodic function of x.
Ignoring what happens for negative values of sin(x), csc(x) is at local minima for maximal values of sin(x), which occur at x = (2k+1/2)pi for i any integer.
Putting the -1 into -1 + csc(x) simply 'lowers' the function without changing the positions of these minima.
PS: Incidentally, using GeoGebra can be a big help in solving problems like these. Free. Easy to use.
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