Скачать или смотреть Graphing Rational Functions | Examples and Steps to Follow

📚 Learn How to Graph Rational Functions Step-by-Step!

In this video, we walk through how to graph rational functions by identifying intercepts, asymptotes, and additional points. You’ll learn to analyze the structure of the function and sketch an accurate graph with all key features clearly labeled.

🔍 What You’ll Learn in This Video:
✅ Steps to Graph a Rational Function:
✔ Find the y-intercept by letting x = 0
✔ Find x-intercepts by solving the numerator = 0
✔ Determine vertical asymptotes by setting the denominator = 0
✔ Analyze the degrees to find horizontal or slant asymptotes
✔ Plot additional points for accuracy and sketch the curve

📊 Examples Included in This Video:
✔ f(x) = (2x²)/(x² – 1)
• Vertical asymptotes: x = –1, x = 1
• Horizontal asymptote: y = 2
• Y-intercept: (0, 0)

✔ f(x) = x/(x² – x – 2)
• Vertical asymptotes: x = –1, x = 2
• Horizontal asymptote: y = 0
• X- and Y-intercepts: (0, 0)

✔ f(x) = (2x² – 2x – 4)/(x² + 8x + 16)
• Vertical asymptote: x = –4
• Horizontal asymptote: y = 2
• X-intercepts: (–1, 0) and (2, 0)
• Y-intercept: (0, –1/4)

By the end of this lesson, you'll be able to:
✔ Identify and graph vertical, horizontal, and slant asymptotes
✔ Find intercepts and additional points
✔ Sketch rational functions accurately

📥 Download Free Guided Notes!
Follow along and practice with structured support:
👉 https://www.understandthemath.com/alg...

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Timestamps
00:00 Introduction
00:19 Steps to Follow
00:31 Example 1
09:50 Example 2
19:03 Example 3

More About Understand The Math
Understand The Math offers clear, accessible, and engaging mathematics instruction for students and lifelong learners. I'm Cheryl Hile, the founder of Understand The Math, with a Ph.D. in Engineering Science and Applied Mathematics and over 25 years of university teaching experience. My goal is to provide accurate, high-quality math instruction through step-by-step explanations and carefully worked-out examples.

Each video includes free guided notes, linked in the description. These notes help students follow along, highlight key concepts, and practice problems, making review easier and more effective.

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