Functions – MCQ Test (Basics)
Based on NCERT Mathematics (Classes 8–11)
Questions
1. A function is:
A) A relation with one input and many outputs
B) A relation with many inputs and one output
C) A relation with exactly one output for each input
D) None of the above
2. Which of the following is a function?
A) {(1,2), (2,3), (1,4)}
B) {(1,2), (2,3), (3,4)}
C) {(1,1), (1,2)}
D) {(2,3), (2,3), (2,4)}
3. If f(x) = x + 2, then f(3) is:
A) 5
B) 6
C) 3
D) 2
4. Which of these rules defines a function?
A) Square a number
B) Choose any prime factor
C) List all factors of a number
D) Pick any divisor
5. The function f(x) = 2x has input 5. What is the output?
A) 7
B) 10
C) 25
D) 15
6. Which pair is not part of a function?
A) (1,2), (2,4), (3,6)
B) (2,3), (2,5)
C) (0,0), (1,1), (2,2)
D) (3,2), (4,2), (5,2)
7. The function f(x)=x^2. What is f(-3)?
A) 9
B) -9
C) 6
D) -6
8. The domain of f(x)=x+5 is:
A) Only natural numbers
B) Real numbers
C) Only positive integers
D) Whole numbers
9. What is the image of 2 under the function f(x)=3x-1?
A) 5
B) 6
C) 7
D) 4
10. Which of the following can represent a real-life function?
A) Name → Age
B) Height → Weight
C) Temperature → Season
D) Roll number → Marks
11. The graph of y=x^2 is a:
A) Straight line
B) Parabola
C) Circle
D) Ellipse
12. Which set represents a function?
A) {(1,2),(2,1),(3,2),(2,4)}
B) {(a,b),(b,a),(a,c)}
C) {(1,1),(2,2),(3,3)}
D) {(x,y),(x,z)}
13. For f(x)=3x+2, what is f(0)?
A) 0
B) 2
C) 3
D) 1
14. The function f(x)=√x is defined only for:
A) All real numbers
B) Positive real numbers
C) Non-negative real numbers
D) Negative numbers only
15. What is the range of f(x)=x^2 for x∈{-2,-1,0,1,2}?
A) {0,1,4}
B) {-4,-1,0,1,4}
C) {0,1,2,3,4}
D) {1,2,3,4}
16. Which graph shows a function?
A) A circle
B) A vertical line
C) A parabola
D) A closed loop
17. The function f(x)=|x| is:
A) Always positive
B) Always increasing
C) Constant
D) Negative for negative x
18. Which of the following is not a function?
A) A mapping of students to their ID numbers
B) Mapping of cities to their populations
C) Mapping of a person to their age
D) Mapping numbers to their divisors
19. If f(x)=x^3, then f(-2)= ?
A) -6
B) -8
C) 8
D) 6
20. The domain of f(x)=1/x is:
A) All real numbers
B) All real numbers except 0
C) Only positive numbers
D) Natural numbers
21. If f(x)=2x+1, then f(f(2)) =
A) 7
B) 9
C) 11
D) 13
22. Which of these functions is linear?
A) x^2 + 1
B) 1/x
C) 2x + 3
D) x^3
23. If f(x)=x^2, then f(a + b) =
A) a^2 + b^2
B) (a + b)^2
C) ab
D) 2ab
24. What is the value of f(x)=4x−3 at x=0?
A) 0
B) -3
C) 3
D) 1
25. A function is one-to-one if:
A) Each input has many outputs
B) Each input has a unique output
C) One output has many inputs
D) None of the above
26. The function f(x)=x^2 - 4 has value 0 at:
A) x=2 only
B) x=-2 only
C) x=±2
D) x=0
27. Which function is even?
A) x^3
B) x^2
C) x
D) √x
28. A function that reflects over the y-axis is:
A) Odd
B) Even
C) Both
D) Neither
29. Which is not a valid function definition?
A) f(x)=1/x
B) f(x)=√(-x)
C) f(x)=x^3
D) f(x)=|x|
30. The composition of functions means:
A) Adding two functions
B) Subtracting two functions
C) Applying one function to the result of another
D) Multiplying two functions
31. The function f(x)=sin x is:
A) Odd
B) Even
C) Neither
D) Constant
32. Which of these functions is injective?
A) f(x)=x^2
B) f(x)=|x|
C) f(x)=x
D) f(x)=sin x
33. A function is onto if:
A) Every output in codomain is mapped by some input
B) One input maps to many outputs
C) All outputs are positive
D) It is linear
34. Domain of f(x)=√(1 − x^2) is:
A) (-∞,∞)
B) [-1,1]
C) (1,∞)
D) [0,∞)
35. If f(x)=log x, domain is:
A) x>0
B) x≥0
C) x<0
D) x∈ℝ
36. The inverse of a function exists only if it is:
A) Many-one
B) One-one and onto
C) Linear
D) Quadratic
37. If f(x)=e^x, it is:
A) Decreasing
B) Constant
C) Increasing
D) Oscillating
38. The graph of an odd function is symmetric about:
A) Y-axis
B) X-axis
C) Origin
D) Line y=x
39. The function f(x)=|x| is
A) Even
B) Odd
C) Periodic
D) Neither
40. If f(x)=ln x, then f(e) equals:
A) 0
B) 1
C) e
D) Cannot be found
41. Let f(x)=5x−4. The inverse function f⁻¹(y) is:
A) (y+4)/5
B) 5y−4
C) (y−4)/5
D) Cannot invert
42. Which of the following functions is neither even nor odd?
A) x^3
B) sin x
C) x + 1
D) cos x
43. For f(x)=1/(x−2), domain is:
A) All real x
B) All real x except 2
C) x>2
D) x<2
44. If f(x)=x^2 and g(x)=x+1, what is (f∘g)(2)?
A) 3
B) 9
C) 4
D) 16
45. A function whose graph passes the Vertical Line Test but fails the Horizontal Line Test
is:
A) Injective
B) Surjective
C) Both injective and surjective
D) Neither injective nor surjective
46. Which pair of functions are inverses on ℝ?
A) y=2x and y=1/(2x)
B) y=x^3 and y=∛x
C) y=e^x and y=ln(x+1)
D) y=x+2 and y=x−2
47. The function f(x)=sin x has period:
A) π
B) 2π
C) π/2
D) No period
48. The range of f(x)=|x| for x∈[-3,4] is:
A) [-3,4]
B) [0,4]
C) [-3,0]
D] [0,3]
49. Which of the following functions is periodic?
A) x
B) |x|
C) tan x
D) x^2
50. The derivative of a function at a point gives its:
A) Area under the curve
B) Rate of change at that point
C) Total integral
D) Domain
Answer Key
1: C 2: B 3: B 4: A 5: B 6: B 7: A 8: B 9: A 10: D
11: B 12: C 13: B 14: C 15: A 16: C 17: A 18: D 19: B 20: B
21: C 22: C 23: B 24: B 25: B 26: C 27: B 28: B 29: B 30: C
31: A 32: C 33: A 34: B 35: A 36: B 37: C 38: C 39: A 40: B
41: C 42: C 43: B 44: B 45: D 46: B 47: B 48: B 49: C 50: B
