Education Technology

Algebra II: Graphs of Rational Functions

by Texas Instruments


  • Students will determine the domain and range of a rational function.
  • Students will describe the end behavior and the graph of a rational function near its asymptote.
  • Students will connect the horizontal translation of a graph of a rational function to its equation.
  • Students will find the equations of a rational function with specified asymptote(s) or restriction(s).


  • end behavior
  • rational function
  • asymptote
  • horizontal shift
  • positive or negative infinity
  • domain and range

About the Lesson

This lesson involves investigating the graphs of rational functions. As a result, students will:

  • Describe the end behavior of the graph of f(x)=1/x and what is happening near the asymptote.
  • Horizontally translate the graph of f(x)=1/x and determine the relationship between the equation of the asymptote and the equation of the rational function.
  • Write the equations of graphs of rational functions with two asymptotes.