BitWithBite
Mathematics Worksheet
🔗 Continuity
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Test whether a function is continuous at a point using the three-part definition.Locate points where a function is discontinuous.Classify discontinuities as removable, jump, or infinite.Use continuity to reason about the existence of roots.🧠 Section A · Concept Check ● BEGINNER 4 × 1 = 4
1Which condition is required for f to be continuous at x = a?
2Where is f(x) = 1/(x + 5) discontinuous?
3f(x) = (x2 − 1)/(x − 1) at x = 1 has a:
4A step function that jumps from 2 to 5 at x = 0 has a:
🧮 Section B · Problem Solving ● INTERMEDIATE 2 + 3×3 = 11
5f is continuous at a if lim(x→a) f(x) = .
6f(x) = 1/(x + 5) is discontinuous at x = .
7Is f(x) = 3x2 + 2x − 1 continuous at x = 1?
8Where is f(x) = 1/(x + 5) discontinuous?
9Is f(x) = √x continuous at x = −1? Why or why not?
🚀 Section C · Challenge ● CHALLENGE 5
10Classify the discontinuity of f(x) = (x2 − 1)/(x − 1) at x = 1.
💭 Reflection — the most useful thing I learned:
A ___/4 B ___/11 C ___/5 Total ___/20
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1-D 2-B 3-C 4-B | 5 f(a) 6 −5 7 = Yes 8 = x = −5 9 = No — √x is undefined for negative x | 10 = Removable (a hole)