Practice these 50 exam-oriented MCQs from Chapter 1 – Functions and Graphs for Class 12 Mathematics (FBISE). Topics include functions, domain, codomain, range, types of functions, composition, inverse functions, basic graphs, algebraic and transcendental functions, modulus, and graph transformations.
1. A function assigns each element of its domain to
A) only an integer B) exactly one value in the codomain C) at least two values D) no value
2. The set of permissible input values is the
A) codomain B) image C) domain D) range
3. The set of possible output values specified for a function is its
A) domain B) inverse C) argument D) codomain
4. The set of actual output values is its
A) range B) domain C) codomain D) preimage
5. If f(x)=2x+3, f(4) equals
A) 5 B) 11 C) 8 D) 10
6. If f(x)=x²−1, f(3) equals
A) 9 B) 10 C) 8 D) 6
7. f(x)=5 is a
A) identity function B) quadratic function C) reciprocal function D) constant function
8. The identity function is
A) f(x)=x B) f(x)=1 C) f(x)=x² D) f(x)=0
9. A function assigning different images to different domain elements is
A) constant B) one-to-one C) many-to-one D) onto only
10. A function whose range equals its codomain is
A) constant B) many-to-one C) onto D) one-to-one only
11. A function that is both one-to-one and onto is
A) constant B) many-to-one C) quadratic D) bijective
12. For f(x)=x² on all real numbers, the range is
A) [0,∞) B) (-∞,∞) C) (-∞,0] D) (0,∞)
13. The domain of f(x)=√x is
A) (0,∞) B) [0,∞) C) (-∞,∞) D) (-∞,0]
14. The domain of f(x)=1/x is
A) x≥0 B) x≤0 C) all real numbers except 0 D) all real numbers
15. The graph of a constant function is
A) a vertical line B) a parabola C) a circle D) a horizontal line
16. The graph of y=x is
A) a straight line through the origin B) a parabola C) a hyperbola D) a circle
17. The graph of y=x² is a
A) hyperbola B) parabola C) straight line D) circle
18. The graph of y=√x lies in
A) the third quadrant only B) the fourth quadrant only C) the first quadrant and includes the origin D) the second quadrant only
19. If f=x+2 and g=3x, (f+g)(x) is
A) 3x+2 B) 4x C) x+6 D) 4x+2
20. If f=x+1 and g=2x, (fg)(x) is
A) 2x²+2x B) 3x+1 C) 2x+1 D) x²+2x
21. If f=x+2 and g=3x, (f∘g)(x) is
A) 3x B) 3x+2 C) 3x+6 D) x+6
22. If f=2x+1 and g=x−3, (g∘f)(x) is
A) 2x−3 B) x−2 C) 2x−2 D) 2x+4
23. An inverse function reverses the
A) domain only B) range only C) coefficient only D) input-output correspondence
24. A function must be one-to-one to have
A) an inverse function B) a domain C) a codomain D) a graph
25. If f(x)=x+5, f⁻¹(x) is
A) 1/(x+5) B) x−5 C) x+5 D) 5−x
26. If f(x)=2x−4, f⁻¹(x) is
A) (x−4)/2 B) 2x−4 C) (x+4)/2 D) 2x+4
27. The domain of a function becomes the ___ of its inverse.
A) codomain B) graph C) constant D) range
28. The range of a function becomes the ___ of its inverse.
A) domain B) codomain C) slope D) zero
29. A function and its inverse are reflections in
A) y=0 B) y=x C) y=−x D) x=0
30. A linear function has the form
A) y=a/x B) y=√x C) y=ax+b D) y=ax²+bx+c
31. For y=3x+2, the slope is
A) 2 B) −3 C) 1 D) 3
32. For y=−2x+5, the y-intercept is
A) 5 B) −2 C) 2 D) −5
33. A quadratic function has the form
A) y=√x B) y=ax²+bx+c, a≠0 C) y=ax+b D) y=a/x
34. The graph of a quadratic function is a
A) straight line B) circle C) parabola D) hyperbola
35. The vertex of y=x² is
A) (1,0) B) (0,1) C) (−1,0) D) (0,0)
36. A reciprocal function has the form
A) y=a/x, a≠0 B) y=ax+b C) y=ax² D) y=√x
37. The graph of y=1/x has
A) three branches B) two branches C) one branch D) no branches
38. A function involving algebraic operations and powers is generally
A) constant B) periodic C) algebraic D) transcendental
39. Which is transcendental?
A) y=x²+1 B) y=3x+2 C) y=√x D) y=e^x
40. For y=a^x, the base must satisfy
A) a>0 and a≠1 B) a=0 only C) a<0 only D) a=1 only
41. For y=log_a x, the conditions are
A) x<0 only B) a>0, a≠1, x>0 C) a<0, x>0 D) a=1, x>0
42. The domain of y=log_a x is
A) x≥0 B) x<0 C) x>0 D) all real x
43. The domain of y=e^x is
A) x>0 only B) x≥0 only C) integers only D) all real numbers
44. The range of y=e^x is
A) (0,∞) B) (-∞,∞) C) [0,∞) D) (-∞,0)
45. The modulus function is
A) y=x² B) y=1/x C) y=√x D) y=
46. The range of y=|x| is
A) (-∞,0] B) (0,∞) C) [0,∞) D) (-∞,∞)
47. The graph of y=|x| is symmetric about the
A) x-axis B) line y=x C) origin D) y-axis
48. Replacing x by x−h shifts f(x)
A) h units right B) h units left C) h units up D) h units down
49. Adding k to f(x) shifts its graph
A) k units left B) k units upward C) k units downward D) k units right
50. Multiplying f(x) by a positive constant greater than 1 gives a
A) reflection B) vertical translation C) vertical stretch D) horizontal translation
Show Result Try Again
Explore More Class 12 Mathematics MCQs
Chapter 1 – Functions and Graphs Chapter 2 – Limit, Continuity and Derivative Chapter 3 – Integration Chapter 4 – Differential Equations Chapter 5 – Kinematics of Motion in a Straight Line Chapter 6 – Analytical Geometry Chapter 7 – Conic Section Chapter 8 – Inverse Trigonometric Functions and Their Graphs Chapter 9 – Solution of Trigonometric Equations Chapter 10 – Numerical Methods
Class 12 Mathematics Main Hub
Class 12 Mathematics Chapter-wise MCQs – FBISE
Class 12 All Subjects Main Hub
Class 12 MCQs – All Subjects | FBISE
Syllabus & SLO Alignment
This set follows the Class 12 Functions and Graphs SLOs covering function as a rule of correspondence; domain, co-domain and range; one-to-one and onto functions; linear, quadratic and square-root functions; inverse functions and their domain and range; graphical representation; algebraic and transcendental functions; exponential and logarithmic functions; modulus; the relation between a one-to-one function and its inverse through a graph; and graph transformations.
Finished the MCQs? Share with your friends!