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 HW Helper P: 1,391 Your function, as written, is just equal to -1, except when $\phi = 1$, where there is a discontinuity because the denominator vanishes there. If you want an example of a function that has a similar form but isn't trivially some constant and has some applications, see Mobius transformation. (But note that the Mobius transformation is usually used with complex numbers. I don't know if it is used much in real number applications).