Rational Functions with two Vertical Asymptotes - Applet

Rational functions with two vertical asymptotes are explored interactively using an applet. The investigation of these functions is carried out by changing parameters included in the formula of the function.

Rational functions is of the form

f(x) = 1 / ((x - a)(x - b))

where the parameters a and b are changed and their effects on the graph in general and the vertical asymptotes in particular are investigated.

Interactive Tutorial

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  1. Click on the button "click here to start", above, to start the applet and maximize the window obtained. The two vertical asymptotes are in red.
  2. Set parameter b to -2 and change parameter a. How does the equation of the vertical asymptote on the left change with changes in parameter a?
  3. Set parameter a to 2 and change parameter b. How does the equation of the vertical asymptote on the right change with changes in parameter b.
  4. Find analytical equations to each of the vertical asymptote and use them to explain the changes in the vertical asymptotes observed when a and b changed values.

More on topics related to rational functions

tutorial on rational functions.

Graphs of rational functions

tutorial on graphs of rational functions

self test on graphs of rational functions.