Grade 12 · Mathematics
Continuity
Why it matters
Continuous functions.
Advanced20m readingPrerequisite: One-sided limits
What does it mean for a function to be continuous?
Short answer
A function is continuous at a point if it has no break there: the function is defined at the point, its limit exists, and the limit equals the function’s value. Informally, you can draw a continuous function without lifting your pen. Breaks come from holes, jumps, or vertical asymptotes, which make the function discontinuous.
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Frequently asked questions
- What are the conditions for continuity at a point?
- The function is defined there, its limit exists there, and the limit equals the function value.
- What kinds of discontinuities are there?
- Removable (a hole), jump (a sudden step), and infinite (a vertical asymptote).