📝 FUNCTIONS DEFINED EXPLICITLY AND IMPLICITLY

📖 From Calculus • 4. Topics in Differentiation • 30 questions available

Practice MCQs for FUNCTIONS DEFINED EXPLICITLY AND IMPLICITLY. Test your knowledge with carefully crafted questions across easy, medium, and hard difficulty levels.

🔄 Last updated: 2026-07-14

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📝 Sample Questions

Q1. Which equation defines \(y\) explicitly as a function of \(x\)?

🔹 A. \(x^2 + y^2 = 4\)

🔹 B. \(y = 3x^2 - 5x + 2\)

🔹 C. \(x^3 + y^3 = 3xy\)

🔹 D. \(xy + \sin y = x\)

💡 Difficulty: easy | ✅ Correct: B

Q2. The graph of \(x = y^2\) fails the vertical line test. This means:

🔹 A. No functions of \(x\) are defined by this equation

🔹 B. The equation defines exactly one function of \(x\)

🔹 C. The equation implicitly defines two functions of \(x\)

🔹 D. The equation cannot be solved for \(y\)

💡 Difficulty: medium | ✅ Correct: C

Q3. The equation \(x^2 + y^2 + 1 = 0\):

🔹 A. Defines infinitely many real functions

🔹 B. Defines one real function of \(x\)

🔹 C. Defines no real functions of \(x\)

🔹 D. Defines two real functions of \(x\)

💡 Difficulty: hard | ✅ Correct: C

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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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