Q1: 1. Which of the following is a relation?

• A) { (1,2), (2,3), (3,4) }
• B) { (2,4), (4,6), (6,8) }
• C) { (1,1), (2,2), (3,3) }
• D) { (1,3), (3,5), (5,7) }

Q2: 2. In a function, each input has how many possible outputs?

• A) One
• B) Two
• C) Three
• D) Four

Q3: 3. Which of the following is a function?

• A) { (1,2), (2,3), (3,2) }
• B) { (2,4), (4,6), (2,6) }
• C) { (1,1), (2,2), (3,3) }
• D) { (1,3), (3,5), (5,7) }

Q4: 4. What is the range of the function f(x) = x^2 ?

• A) All real numbers
• B) Positive real numbers
• C) Negative real numbers
• D) Non-negative real numbers

Q5: 5. Which of the following functions is not injective?

• A) f(x) = x + 3
• B) g(x) = x^2
• C) h(x) = |x|
• D) k(x) = 2x

Q6: 6. If f(x) = 2x - 1 and g(x) = 3x + 2, what is (f ∘ g)(x)?

• A) 6x + 1
• B) 6x + 5
• C) 5x + 1
• D) 5x + 5

Q7: 7. Which of the following is an example of a bijective function?

• A) f(x) = x^2
• B) g(x) = 2x + 1
• C) h(x) = e^x
• D) k(x) = 3x - 2

Q8: 8. If f(x) = 2x and g(x) = x^2, what is (g ∘ f)(x)?

• A) 4x^2
• B) 4x
• C) 2x^2
• D) 2x

Q9: 9. Which of the following is an example of a reflexive relation?

• A) { (1,1), (2,2), (3,4) }
• B) { (1,2), (2,1), (3,3) }
• C) { (1,2), (2,3), (3,1) }
• D) { (1,1), (2,2), (3,3) }

Q10: 10. What is the domain of the function f(x) = √(4 - x^2) ?

• A) x ≤ 2
• B) x ≥ -2
• C) -2 ≤ x ≤ 2
• D) x > 2

Q11: 11. Which of the following is true for an onto function?

• A) Every element in the codomain is the image of at least one element in the domain.
• B) Every element in the domain is the image of at least one element in the codomain.
• C) Every element in the domain is the image of exactly one element in the codomain.
• D) Every element in the codomain is the image of exactly one element in the domain.

Q12: 12. Given the functions f(x) = 2x + 3 and g(x) = x^2 - 1, what is (f ∘ g)(x)?

• A) 2x^2 + 5
• B) 2x^2 + 1
• C) x^2 + 5
• D) x^2 + 1

Q13: 13. Which of the following represents an injective function?

• A) f(x) = x^2
• B) g(x) = x + 1
• C) h(x) = 3x
• D) k(x) = √x

Q14: 14. If f(x) = x + 2 and g(x) = 2x - 1, what is (g ∘ f)(x)?

• A) 2x + 1
• B) 2x + 3
• C) x + 3
• D) x + 1

Q15: 15. Which of the following is an example of a surjective function?

• A) f(x) = x^2
• B) g(x) = 2x + 1
• C) h(x) = e^x
• D) k(x) = 3x - 2

Q16: 16. If f(x) = x^2 and g(x) = 3x, what is (f ∘ g)(x)?

• A) 9x^2
• B) 3x^2
• C) 3x
• D) x^2

Q17: 17. Which of the following is an example of a symmetric relation?

• A) { (1,1), (2,2), (3,3) }
• B) { (1,2), (2,1), (3,4) }
• C) { (1,2), (2,1), (2,3) }
• D) { (1,2), (2,1), (1,3) }

Q18: 18. What is the range of the function f(x) = 1/x ?

• A) All real numbers
• B) Positive real numbers
• C) Negative real numbers
• D) Non-zero real numbers

Q19: 19. Which of the following is not a function?

• A) { (1,2), (2,3), (1,3) }
• B) { (2,4), (4,6), (6,8) }
• C) { (1,1), (2,2), (3,3) }
• D) { (1,3), (3,5), (5,7) }

Q20: 20. If f(x) = 3x - 2 and g(x) = x^2 + 1, what is (f ∘ g)(x)?

• A) 3x^2 - 5
• B) 3x^2 + 1
• C) x^2 - 5
• D) x^2 + 1

Q21: 21. Which of the following is an example of a transitive relation?

• A) { (1,1), (2,2), (3,3) }
• B) { (1,2), (2,3), (1,3) }
• C) { (1,2), (2,3), (3,4) }
• D) { (1,2), (2,3), (1,4) }

Q22: 22. What is the domain of the function f(x) = √(x + 5) ?

• A) x ≥ -5
• B) x > -5
• C) x ≥ 0
• D) x > 0

Q23: 23. Which of the following is true for a one-to-one function?

• A) Every element in the codomain is the image of at least one element in the domain.
• B) Every element in the domain is the image of at least one element in the codomain.
• C) Every element in the domain is the image of exactly one element in the codomain.
• D) Every element in the codomain is the image of exactly one element in the domain.

Q24: 24. Given the functions f(x) = x + 1 and g(x) = 2x - 3, what is (f ∘ g)(x)?

• A) 2x - 2
• B) 2x - 4
• C) x - 2
• D) x - 4

Q25: 25. Which of the following represents a surjective function?

• A) f(x) = x^2
• B) g(x) = x + 1
• C) h(x) = 3x
• D) k(x) = |x|