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Function be continuous and discontinuous

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Problem 3:
Explain why this is no good as a definition of continuity at a point a (either by giving an example of a continuous function that does not satisfy the definition or a discontinuous one that does):
Given  > 0 there exists a  > 0 such that |x - a| <   |f(x) - f(a)| < 

Problem 4:
Can a function be continuous at one value of x and discontinuous at all other
x  R? Explain your answer, giving proofs where appropriate.

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https://brainmass.com/math/graphs-and-functions/function-continuous-discontinuous-449229

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Problem 3:
Explain why this is no good as a definition of continuity at a point a (either by giving an example of a continuous function that does not satisfy the definition or a discontinuous one that does):
Given e > 0 there exists a d > 0 such that |x ...

Solution Summary

The expert determines if some functions can be continuous and discontinuous at different regions.

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