Rational Functions
A rational function is the quotient of two polynomials. The behaviour of a rational function can change dramatically with small changes in a single parameter. Watch what happens as the coefficient of x3 in the denominator changes.
To understand this graph fully, plot the denominator kx3 - 3x + 2 with k varying from -4 to +4. Pay close attention to the denominator's roots in relation to the poles of our rational function animation above.