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Relations and Functions

This quiz covers the fundamental concepts of relations and functions, including their properties, types, and applications.

14 Questions Published
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Questions

Question 1 Multiple Choice (Single Answer)

Which of the following is NOT a property of a relation?

  1. Reflexivity
  2. Symmetry
  3. Transitivity
  4. Injectivity
Question 2 Multiple Choice (Single Answer)

Given the relation (R = {(1, 2), (2, 3), (3, 4)}, what is the domain of (R)?

  1. {1, 2, 3}
  2. {2, 3, 4}
  3. {1, 2, 3, 4}
  4. {1, 3}
Question 3 Multiple Choice (Single Answer)

Which of the following is an example of a function?

  1. \(f(x) = x^2\)
  2. \(R = \{(1, 2), (2, 3), (3, 4)\}
  3. \(S = \{(1, 2), (2, 3), (3, 2)\}
  4. \(T = \{(1, 2), (1, 3), (2, 4)\}
Question 4 Multiple Choice (Single Answer)

What is the range of the function (f(x) = 2x + 1) when the domain is ({1, 2, 3})?

  1. {3, 5, 7}
  2. {1, 3, 5}
  3. {2, 4, 6}
  4. {0, 2, 4}
Question 5 Multiple Choice (Single Answer)

Which of the following functions is injective?

  1. \(f(x) = x^2\)
  2. \(f(x) = |x|\)
  3. \(f(x) = 2x + 1\)
  4. \(f(x) = x + sin(x)\)
Question 6 Multiple Choice (Single Answer)

Which of the following functions is surjective?

  1. \(f(x) = x^2\)
  2. \(f(x) = |x|\)
  3. \(f(x) = 2x + 1\)
  4. \(f(x) = x + sin(x)\)
Question 7 Multiple Choice (Single Answer)

Which of the following functions is bijective?

  1. \(f(x) = x^2\)
  2. \(f(x) = |x|\)
  3. \(f(x) = 2x + 1\)
  4. \(f(x) = x + sin(x)\)
Question 8 Multiple Choice (Single Answer)

What is the inverse of the function (f(x) = 3x - 2)?

  1. \(f^{-1}(x) = \frac{x + 2}{3}\)
  2. \(f^{-1}(x) = \frac{x - 2}{3}\)
  3. \(f^{-1}(x) = \frac{1}{3}x + 2\)
  4. \(f^{-1}(x) = \frac{1}{3}x - 2\)
Question 9 Multiple Choice (Single Answer)

Which of the following relations is an equivalence relation?

  1. Congruence modulo 5
  2. Divisibility by 2
  3. Parallelism of lines
  4. Similarity of triangles
Question 10 Multiple Choice (Single Answer)

What is the composition of the functions (f(x) = x^2) and (g(x) = x + 1)?

  1. \(h(x) = x^2 + 1\)
  2. \(h(x) = x^2 + 2x + 1\)
  3. \(h(x) = x^3 + x + 1\)
  4. \(h(x) = x^3 + 2x^2 + 1\)
Question 11 Multiple Choice (Single Answer)

Which of the following is an example of a many-to-one function?

  1. \(f(x) = x^2\)
  2. \(f(x) = |x|\)
  3. \(f(x) = 2x + 1\)
  4. \(f(x) = \lfloor x \rfloor\)
Question 12 Multiple Choice (Single Answer)

Which of the following is an example of a one-to-many function?

  1. \(f(x) = x^2\)
  2. \(f(x) = |x|\)
  3. \(f(x) = 2x + 1\)
  4. \(f(x) = sin(x)\)
Question 13 Multiple Choice (Single Answer)

What is the domain of the function (f(x) = \frac{1}{x})?

  1. {0}
  2. All real numbers except 0
  3. {1}
  4. {2}
Question 14 Multiple Choice (Single Answer)

Which of the following functions is continuous at (x = 0)?

  1. \(f(x) = x^2\)
  2. \(f(x) = |x|\)
  3. \(f(x) = \frac{1}{x}\)
  4. \(f(x) = sin(x)\)
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