Continuity of Functions

Grade 12 Maths — Continuity of Functions: 25 practice questions with instant scoring and explanations.

1. A function f is continuous at x = a if:
2. The function f(x) = |x| at x = 0 is:
3. A function f is continuous on [a, b] if it is continuous at:
4. Which of the following is discontinuous at x = 1?
5. The function f(x) = ⌊x⌋ (greatest integer) is discontinuous at:
6. If f and g are continuous at x = a, then f + g is:
7. If f and g are continuous at x = a, then f × g is:
8. If f is continuous at x = a and g is continuous at f(a), then g ∘ f is:
9. Which theorem states that a continuous function on [a, b] attains its maximum and minimum?
10. The Intermediate Value Theorem states that if f is continuous on [a, b] and f(a) < k < f(b), then:
11. A removable discontinuity at x = a means:
12. A jump discontinuity occurs when:
13. The function f(x) = sin(1/x) for x ≠ 0 and f(0) = 0 has:
14. If f is continuous at x = a and f(a) ≠ 0, then there exists δ > 0 such that:
15. All polynomial functions are:
16. The exponential function eˣ is:
17. For continuity at x = a, we need: lim(x→a) f(x) exists AND:
18. The function f(x) = (x² − 1)/(x − 1) for x ≠ 1 and f(1) = 2 is:
19. If f is continuous and one-one on [a, b], then f⁻¹ is:
20. For the piecewise function f(x) = {x if x ≤ 1, 3 − x if x > 1} at x = 1:
21. Rational functions are continuous:
22. The logarithmic function ln(x) is continuous on:
23. By the Intermediate Value Theorem, the equation x³ − 2x − 5 = 0 has a solution in:
24. f(x) = x² is continuous:
25. f(x) = 1/x is NOT continuous at: