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Rational Function Multiplicity of Zeros, Vertical Asymptotes

Sliding each t_n will change the value of a factor on top (or a zero/hole) along with its multiplicity. Sliding each b_n will change the value of a factor on bottom (or a vertical asymptote/hole) along with its multiplicity. Try to determine the properties of the rational function, particularly those associated with the multiplicity of each factor.
Matt James Lincoln Southwest High School Lincoln, NE mjames2@lps.org