Hey, everyone. By now, we've worked with a bunch of different polynomial functions, things like
- 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
Introduction to Rational Functions: Study with Video Lessons, Practice Problems & Examples
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Rational functions are formed by placing polynomials in the numerator and denominator, represented as p(x) / q(x). The domain is restricted where the denominator equals zero, requiring careful evaluation. For example, for the function f(x) = x + 5x² - 25, the domain excludes 5 and -5. Simplifying involves factoring and canceling common terms, ensuring domain restrictions are identified before simplification.
Intro to Rational Functions
Video transcript
Find the domain of the rational function. Then, write it in lowest terms.
f(x)=x−3x2+9
{x∣x≠0},
{x∣x≠3},
{x∣x≠−3},
{x∣x≠3},
Find the domain of the rational function. Then, write it in lowest terms.
f(x)=2x2−86x5
Do you want more practice?
More setsHere’s what students ask on this topic:
What is a rational function in algebra?
A rational function in algebra is a function that can be expressed as the ratio of two polynomials. It is written in the form
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How do you find the domain of a rational function?
To find the domain of a rational function, identify the values of
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How do you simplify a rational function?
To simplify a rational function, factor both the numerator and the denominator to identify and cancel out common factors. For example, consider the function
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Why is it important to find the domain before simplifying a rational function?
It is important to find the domain before simplifying a rational function because simplifying can sometimes remove factors that indicate domain restrictions. For example, in the function
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What are common mistakes to avoid when working with rational functions?
Common mistakes when working with rational functions include: 1) Not finding the domain before simplifying, which can lead to missing domain restrictions. 2) Incorrectly factoring polynomials in the numerator or denominator. 3) Forgetting to cancel common factors completely. 4) Assuming the simplified function has the same domain as the original without checking. Always ensure you find the domain first, factor correctly, and verify the domain after simplification.
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