Rational Functions with Slant Asymptotes - Applet

Rational functions with slant 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) = (ax2 + 1) / (x + d)

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

Interactive Tutorial

Click on the button "click here to start", above, to start the applet and maximize the window obtained. The vertical asymptote is in red and the slant asymptote is in green.

Set parameter b to 1 and change parameter a. What is the sign of the slope odf the slant asymptote when parameter a is negative? What is the sign of the slope when parameter a is negative? Explain the change of sign of the slope with the change in the sign of a.

Set parameter a to 1 and change parameter b. Does the slope change? Describe the change in the y intercept as parameter b changes.

Find an analytical equation to the slant asymptote and use it to explain the changes observed when first a and b changed values.