- 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
- 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.