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📝 Graphing Rational Functions

📖 From Calculus • 5. The derivative in graphing and applications • 27 questions available

Practice MCQs for Graphing Rational Functions. Test your knowledge with carefully crafted questions across easy, medium, and hard difficulty levels.

🔄 Last updated: 2026-07-15

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📝 Sample Questions

Q1. Identify the vertical asymptote of the function \(f(x)=\dfrac{2x}{x-3}\).

🔹 A. x = 3

🔹 B. x = 2

🔹 C. y = 3

🔹 D. None of the above

💡 Difficulty: easy | ✅ Correct: A

Q2. Find the \(x\)-intercept and \(y\)-intercept of \(f(x)=\dfrac{x^{2}-9}{x+3}\).

🔹 A. \(x=3,\; y=-3\)

🔹 B. \(x=-3,\; y=3\)

🔹 C. \(x=3,\; y=0\)

🔹 D. \(x=0,\; y=-3\)

💡 Difficulty: medium | ✅ Correct: D

Q3. Determine the slant asymptote, holes, and vertical asymptotes for \(f(x)=\dfrac{x^{3}-3x^{2}+2x}{x^{2}-4}\).

🔹 A. Slant \(y=x-3\); hole at \((2,0.5)\); vertical asymptote \(x=-2\)

🔹 B. Slant \(y=x-1\); holes at \(x=2\) and \(x=-2\)

🔹 C. No slant asymptote; vertical asymptotes at \(x=±2\)

🔹 D. Horizontal asymptote \(y=0\)

💡 Difficulty: hard | ✅ Correct: A

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🔗 Related Topics

📝 Approximating Roots 📝 Areas and Limits 📝 Continuity in Applications 📝 Continuity of Compositions 📝 Continuity of Inverse Functions

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