The fraction (ax + b)/(cx + d): domain and graph

MathematicsAlgebraAges 13–14

Graphs the value of the rational expression y = (ax + b)/(cx + d) as x varies. Students drag the sliders a, b, c, d and drag point P along the graph to see the value of the expression at a specific x; the simulation states the domain condition cx + d ≠ 0, the vertical asymptote x = −d/c, the horizontal asymptote y = a/c, and the case where the expression simplifies (ad − bc = 0).