Range of Rational Functions Without Common Roots | Linear & Quadratic Cases Explained

Описание: Confused about how to find the range of rational functions when there are no common roots in the numerator and denominator? This video simplifies the concept for both:

🔹 Linear over quadratic rational functions
🔹 Quadratic over quadratic rational functions

In this lesson, you'll learn:

How to handle rational functions without factor cancellation

Smart techniques to find the range analytically

Key steps using algebra and graph-based intuition

How to use sign charts and derivative tools (where needed)

Perfect for:
✅ Class 11 & 12 students (CBSE/ICSE)
✅ JEE, NEET, and other competitive exams
✅ College algebra learners

📌 Chapters:
00:00 - Intro to Rational Functions
01:15 - Linear over Quadratic Example
06:30 - Quadratic over Quadratic (No Common Root)
11:40 - Range Techniques Recap

📚 Related Topics: Domain and range, vertical asymptotes, critical points, rational inequalities.

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