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Mathematics

Holes and vertical asymptotes

A canceled denominator factor can produce a hole, while an uncanceled zero of the denominator produces a vertical asymptote.

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Chapter 12: Polynomial, absolute-value, and rational functions11 lessons · 43 min
  1. 1Polynomial zeros and multiplicity4 min
  2. 2Polynomial end behavior3 min
  3. 3Polynomial sign intervals4 min
  4. 4Polynomial degree and turning points3 min
  5. 5Absolute-value graph transformations4 min
  6. 6Absolute value as a piecewise function4 min
  7. 7Rational expression restrictions3 min
  8. 8Holes and vertical asymptotes4 min
  9. 9Horizontal asymptotes4 min
  10. 10Domain and range of nonlinear models4 min
  11. 11Challenge: Polynomial, absolute-value, and rational functions6 min
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This lesson is part of the Mathematics course.

Example plan3 lessons · 11 min

Rational expression restrictions3 min
Holes and vertical asymptotesPolynomial, absolute-value, and rational functions4 min
Horizontal asymptotesPolynomial, absolute-value, and rational functions4 min

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