Algebra II: Graphs of Rational Functions

Objectives

• 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).

Vocabulary

• 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.