College Algebra Module 10 Rational and Radical Functions
College Algebra Module 10: Rational and Radical Functions
Module Learning Outcomes: Rational and Radical Functions • • • Introduction to Rational Functions Introduction to Radical Functions Introduction to Variation
Rational Functions
Learning Outcomes: Rational Functions Introduction to Rational Functions • Use arrow notation • Solve applied problems involving rational functions • Find the domains of rational functions • Identify vertical asymptotes • Identify horizontal asymptotes • Graph rational functions
Rational Function •
The Graphs of Toolkit Rational Functions •
Arrow Notation • Symbol Meaning the output approaches infinity (the output increases without bound) the output approaches negative infinity (the output decreases without bound) the output approaches a
Vertical Asymptote •
Desmos Interactive Topic: domain and its effect on vertical asymptotes https: //www. desmos. com/calculator/sxxheguz 0 j
Horizontal Asymptote •
Horizontal Asymptotes of Rational Functions •
Removable Discontinuities •
Intercepts of Rational Functions •
Graphing Rational Functions •
Graphing Rational Functions (cont. ) 6. For factors in the denominator common to factors in the numerator, find the removable discontinuities by setting those factors equal to 0 and then solve 7. Compare the degrees of the numerator and the denominator to determine the horizontal or slant asymptotes 8. Graph
Radical Functions
Learning Outcomes: Radical Functions Introduction to Radical Functions • Find the inverse of a polynomial function • Restrict the domain to find the inverse of a polynomial function
Writing Rational Functions from Intercepts & Asymptotes •
Writing Rational Functions from Their Graphs •
Inverse Polynomial Functions •
Restricting the Domain •
Inverse of a Radical Function •
Variation
Learning Outcomes: Variation Introduction to Variation • Solve direct variation problems • Solve inverse variation problems • Solve problems involving joint variation
Direct Variation •
Inverse Variation •
Joint Variation •
Quick Review • • What is arrow notation used to indicate? Where would you find vertical asymptotes on the graph of a rational function? What is a removable discontinuity? What are the steps in graphing a rational function? How do you find the inverse of a polynomial function? What is the inverse of a quadratic function? What is the relationship when one quantity is a constant divided by another quantity?
- Slides: 28