RELATIONS

30 High School Mathematics Questions on Relations

1. Define a relation in mathematics and give two examples.
2. What is the domain of the relation \( R = \{(2,3), (4,5), (6,7)\} \)?
3. What is the range of the relation \( R = \{(1,4), (3,6), (5,8)\} \)?
4. From the set \( A = \{1, 2, 3\} \) and \( B = \{a, b\} \), list all possible relations from A to B.
5. Is the relation \( \{(2,3), (2,5)\} \) a function? Explain.
6. State whether the relation \( y = x^2 \) is a function. Justify your answer.
7. Plot and shade the region satisfying \( y \leq 2x + 1 \).
8. Plot and shade the region defined by \( y > x - 3 \).
9. State the domain and range of the function \( f(x) = \sqrt{x - 1} \).
10. Determine the domain and range of \( f(x) = \frac{1}{x+2} \).
11. Sketch the graph of the relation \( y = |x| \) and state its domain and range.
12. Draw the graph of the function \( y = 2x - 1 \). Label the intercepts.
13. Describe the domain and range of the relation \( y = x^2 - 4 \).
14. Is the vertical line test used to determine a function or a relation? Explain.
15. Draw a graph of the inequality \( y < -x + 3 \) on the Cartesian plane.
16. Plot the region defined by \( y \geq \frac{1}{2}x - 2 \).
17. Given the relation diagram below from Set A to Set B, identify whether it is a function or not:
    
    Set A: {1, 2, 3} → Set B: {a, b}
    
    
18. What is a one-to-one relation? Give an example.
19. Give an example of a many-to-one relation and explain.
20. Is the relation \( y = \sqrt{x} \) defined for all real numbers? Explain.
21. Sketch the graph of \( y = -x^2 + 4 \) and state its domain and range.
22. Plot the region defined by the system of inequalities: \( y \leq 2x + 1 \) and \( y \geq x - 1 \).
23. What is the inverse of the relation \( R = \{(1,2), (3,4), (5,6)\} \)?
24. Does the relation \( R = \{(1,2), (2,3), (3,1)\} \) represent a function? Why?
25. Find the domain of the relation \( f(x) = \frac{x+1}{x^2 - 4} \).
26. Sketch the graph of \( y = \frac{1}{x} \). State domain and range.
27. Shade the region defined by \( x + y \leq 5 \).
28. Shade the region that satisfies both: \( x > 0 \) and \( y < 3x \).
29. Determine the range of \( y = 3x + 2 \) if the domain is \( \{-2, 0, 1\} \).
30. Sketch the graph of \( y = x^2 \) for \( x \in [-3, 3] \).