Horizontal Asymptotes of Rational Functions
1. Graph the following function: a) What is the degree of the numerator? b) What is the degree of the denominator? c) Describe the end behavior of the graph.
2. Graph the following function: a) What is the degree of the numerator? b) What is the degree of the denominator? c) Describe the end behavior of the graph.
3. Graph the following function: a) What is the degree of the numerator? b) What is the degree of the denominator? c) Describe the end behavior of the graph.
4. Examine your results from questions 1-3. Do these graphs have a horizontal asymptote? Explain your reasoning.
5. Graph the following function: a) What is the degree of the numerator? b) What is the degree of the denominator? c) Describe the end behavior of the graph.
6. Graph the following function: a) What is the degree of the numerator? b) What is the degree of the denominator? c) Describe the end behavior of the graph.
7. Graph the following function: a) What is the degree of the numerator? b) What is the degree of the denominator? c) Describe the end behavior of the graph.
8. Examine your results from questions 5-7. Do these graphs have a horizontal asymptote? Explain your reasoning.
9. Graph the following function: a) What is the degree of the numerator? b) What is the degree of the denominator? c) Describe the end behavior of the graph.
10. Graph the following function: a) What is the degree of the numerator? b) What is the degree of the denominator? c) Describe the end behavior of the graph.
11. Graph the following function: a) What is the degree of the numerator? b) What is the degree of the denominator? c) Describe the end behavior of the graph.
12. Examine your results from questions 9-11. Do these graphs have a horizontal asymptote? Explain your reasoning.