Why do you think a removable discontinuity (hole) doesn't produce an asymptote on the graph of a polynomial function, even though it is excluded from the domain of the function?

  A polynomial function can't have a discontinuity. The domain for all polynomials is all real numbers. 

An example of a discontinuity is where the denominator is zero, e.g. y = 1/x is undefined where x = 0 

An example of a removable discontinuity is where the same factor appears in both the numerator and denominator, e.g. y = x/x is undefined where x = 0 but has no asymptote.

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