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. Here we graph
| y = |
x2 + x + 1
kx3 - 3x + 2 |
with k varying from -3 to +5. Note the horizontal asymptote changing to
oblique when k=0. Find the oblique asymptote and explain why this happens.
To understand this graph fully, plot an animated graph of the denominator
kx3 - 3x + 2
with k running from -4 to +4. Pay close attention to
the denominator's roots in relation to the poles of our rational function animation above.