Homographic function

The homographic function $y=\frac{ax+b}{cx+d}$ is the “functional” face of the rectangular hyperbola: its graph is in fact a rectangular hyperbola with asymptotes parallel to the Cartesian axes. One learns to read off its asymptotes and centre of symmetry directly from the coefficients, studies a complete example with the intersections with the axes, and sees the trick of the division between polynomials to recognise its structure at a glance.

• Definition of the homographic function
• Asymptotes and centre of symmetry
• Example — studying a homographic function
• The polynomial division trick