Asymptotes Part 1

Описание: This series of videos are explaining
The definition of Asymptote and
The three types of Asymptotes
With examples for each
.
.
These links to watch this playlist (Asymptotes):
Asymptotes Part 1
   • Asymptotes Part 1  
Asymptotes Part 2
   • Asymptotes Part 2  
Asymptotes Part 3
   • Asymptotes Part 3  
Asymptotes Part 4
   • Asymptotes Part 4  


Here is a list of topics:
1. Horizontal and Vertical Asymptotes Review
2. Setting the Denominator Equal to Zero to Find The Vertical Asymptote
3. Top Heavy vs Bottom Heavy Functions - Comparing the Degree of The Numerator with the Denominator of the Fraction to Identify the Horizontal Asymptotes
4. Horizontal Asymptotes and End Behavior - As x approaches Infinity
5. Using Long Division To Find The Equation of The Slant / Oblique Asymptote
6. Graphing Rational Functions Using X and Y Intercepts
7. How To Identify and Remove any Holes or Points of Discontinuity
8. Point Discontinuity vs Infinite Discontinuity
9. Domain and Range of Rational Functions
10. Removing the Vertical Asymptote and X Coordinate of the Hole from the Domain
11. Removing the Horizontal Asymptote and Y Coordinate of the Hole from the Range
12. How To Determine / Calculate the X and Y Intercepts of a Rational Expression


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The degree of a function is the highest power of x that appears in the polynomial. To find the horizontal asymptote, there are three easy cases. 1) If the degree of the numerator expression is less than the degree of the denominator expression, then the horizontal asymptote is y=0 (the x-axis). 2) If the degree of the numerator is equal to the degree of the denominator, then you can find the horizontal asymptote by dividing the first, highest term of the numerator by the first, highest term of the denominator. This will simplify to y = some constant (just a number). 3) If the degree of the numerator is greater than the degree of the denominator, then there is no horizontal asymptote.

تعرف على كيفية العثور على الخطوط المقاربة الرأسية / الأفقية للدالة. الخط المقارب هو خط يقترب منه الرسم البياني للوظيفة ولكنه لا يلمسه أبدًا. الخط المقارب العمودية هو خط عمودي يقترب منه الرسم البياني للوظيفة ولكنه لا يلمسها أبدًا. للعثور على الخطوط المقاربة الرأسية (s) للوظيفة العقلانية ، قمنا بتعيين المقام الذي يساوي 0 وحل لـ x.

الخط التقارب الأفقي هو خط أفقي يقترب منه الرسم البياني للوظيفة لكنه لا يتقاطع أبدًا (على الرغم من أنه يعبر عنها أحيانًا). تحتوي الدالة العقلانية على خط تقارب أفقي لـ y = 0 عندما تكون درجة البسط أقل من درجة المقام. دالة عقلانية لها خط تقارب أفقي لـ y = c ، (حيث c هي نسبة المعامل الرئيسي للبسط و المقام) عندما تكون درجة البسط مساوية لدرجة القاسم. دالة عقلانية ليس لها خط تقارب أفقي إذا كانت درجة البسط أكبر من درجة المقام.
taearaf ealaa kayfiat aleuthur ealaa alkhutut almuqarabat alraasiat / al'ufaqiyat lldal. alkhatu almaqarib hu khatun yaqtarib minh alrasm albayaniu lilwazifat walakunah la yalmasuh abdana. alkhatu almaqarib aleumudiat hu khatun eumudiin yaqtarib minh alrasm albayaniu lilwazifat walakunah la yalmasuha abdana. lileuthur ealaa alkhutut almuqarabat alraasia (s) lilwazifat aleuqlaniat , qumna bitaeyin almaqam aldhy yusawi 0 wahala l x.
alkhatu altaqarub al'ufqiu hu khatun 'ufaqiin yaqtarib minh alrasm albianiu lilwazifat lakunah la yataqatae abdana (ela alrghm mn 'anah yaebur eanha ahyanana). tahtawi alddalat aleuqlaniat ealaa khati tuqarib 'ufqi l y = 0 eindama takun darajat albast 'aqala min darajat almaqam. dalat euqlaniat laha khatun tuqarib 'ufqi l y = c , (hith c hi nisbat almaeamil alrayiysii lilbist w almaqama) eindama takun darajat albast musawayatan lidarajat alqasima. dalatan euqlaniatan lays laha khatun tuqarib 'ufqi 'iidha kanat darajat albast 'akbar min darajat almaqam.