Rational Function Grapher

Choose numerator and denominator factors and see which ones become vertical asymptotes, which cancel into holes, and what the degrees do to the ends.

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Used in these lessons

Build a polynomial from its zeros, change each multiplicity, and watch the curve cross, bounce or flatten while the end behaviour follows the degree.

Shrink the interval h and watch the average rate of change converge on the instantaneous rate, with the difference quotient updating as you go.