Table of contents
- 0. Review of Algebra4h 16m
- 1. Equations & Inequalities3h 18m
- 2. Graphs of Equations43m
- 3. Functions2h 17m
- 4. Polynomial Functions1h 44m
- 5. Rational Functions1h 23m
- 6. Exponential & Logarithmic Functions2h 28m
- 7. Systems of Equations & Matrices4h 6m
- 8. Conic Sections2h 23m
- 9. Sequences, Series, & Induction1h 19m
- 10. Combinatorics & Probability1h 45m
5. Rational Functions
Asymptotes
6:47 minutes
Problem 74
Textbook Question
Textbook QuestionSolve each problem. Work each of the following. Find an equation for a possible corresponding rational function.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Rational Functions
A rational function is a function that can be expressed as the ratio of two polynomials, typically in the form f(x) = P(x)/Q(x), where P(x) and Q(x) are polynomials. Understanding the structure of rational functions is essential for identifying their properties, such as asymptotes, intercepts, and behavior at infinity.
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Polynomial Functions
Polynomial functions are mathematical expressions involving variables raised to whole number powers, combined using addition, subtraction, and multiplication. They form the numerator and denominator of rational functions, and their degree and coefficients significantly influence the function's graph and behavior.
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Finding Equations
Finding an equation for a rational function involves determining the appropriate polynomials for the numerator and denominator based on given conditions or characteristics. This process may include identifying roots, vertical and horizontal asymptotes, and ensuring the function meets specific criteria, such as passing through certain points.
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