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Precalculus Mathematics Homework Help
How to determine a hole in a graph?
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[QUOTE="PWiz, post: 4980622, member: 536763"] Adding to what Stephen said, explicit non-polynomial functions containing terms of the type ##u^{-|R|}## (where ##u## is an expression containing ##x##) have "holes" in their graphs if ##u=0## for any real x value . The simplest function of this type is ##y=x^{-1}## (u=x here) which has an asymptote at x=0. Similarly, by letting u=cos x and R=1 , the function will have multiple "holes" arranged in a recurring fashion wherever cos x = 0 (this will be the natural domain of sec x). I also must add that the concept is not just limited to fractions containing x terms in the denominator, but also logarithmic functions, where ##log_a u## is not defined for any x value where u=0. [/QUOTE]
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How to determine a hole in a graph?
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