Removable and Nonremovable Discontinuities in a Rational Function Calculus Example  Summary and Q&A
TL;DR
Learn about the difference between removable and nonremovable discontinuities in rational functions.
Key Insights
 🕳️ Removable discontinuities occur when there are cancellations in a rational function, resulting in holes in the graph.
 🕳️ Holes in rational functions are always removable.
 🚦 Nonremovable discontinuities in rational functions are vertical asymptotes, occurring when the denominator becomes zero.
 🚦 Vertical asymptotes are always nonremovable.
 #️⃣ Rational functions are polynomials over polynomials, with whole number coefficients.
 🍉 Removable discontinuities can be identified by cancelled terms in the function.
 😫 Vertical asymptotes can be found by setting the denominator of the rational function equal to zero.
Transcript
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Questions & Answers
Q: What are removable and nonremovable discontinuities?
Removable discontinuities are holes in a rational function, while nonremovable discontinuities are vertical asymptotes.
Q: How can one identify a removable discontinuity in a rational function?
If there is a cancellation that results in a hole, it is a removable discontinuity. It is represented as a fraction where the numerator and denominator have a common factor.
Q: Are all holes in rational functions removable?
Yes, all holes in rational functions are removable. This means that they can be filled by simplifying the function.
Q: What determines a nonremovable discontinuity in a rational function?
Nonremovable discontinuities in rational functions are vertical asymptotes. They occur where the denominator of the function becomes zero.
Summary & Key Takeaways

Removable discontinuities refer to holes in a rational function, while nonremovable discontinuities refer to vertical asymptotes.

Holes in rational functions are always removable, while vertical asymptotes are always nonremovable.

Rational functions are polynomials over polynomials, with powers of x and whole number coefficients.