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Tracy18
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Continuous, discontinuous and piece-wise function
- MHB
- Thread starter Tracy18
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In summary, a continuous function is one that has no abrupt changes or breaks in its graph and can be drawn without lifting the pencil from the paper. On the other hand, a discontinuous function has abrupt changes or breaks in its graph and cannot be drawn without lifting the pencil from the paper. A piece-wise function is defined by different equations for different intervals or "pieces" of the input, meaning it has a different rule for different parts of its domain. To determine if a function is continuous, one can check if it has a smooth, unbroken graph with no gaps or jumps, or if it passes the "pencil test". It is not possible for a function to be both continuous and discontinuous, as it can only have one
- #2
Prove It
Gold Member
MHB
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Have you tried anything?
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Tracy18
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Nope I don't know where to stat
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What are the three types of discontinuites?Tracy18 said:
-Dan
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HOI
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It is very strange that this says "should have two continuous point(s)". This function will necessarily have infinitely many points of continuity! I presume it means that two of the five break points are to be points of continuity.
FAQ: Continuous, discontinuous and piece-wise function
What is a continuous function?
A continuous function is a type of mathematical function that has no abrupt changes or breaks in its graph. This means that the function is defined for all values within its domain and has a smooth, unbroken curve. In other words, if you were to draw the graph of a continuous function without lifting your pencil, it would be a single, continuous line.
What is a discontinuous function?
A discontinuous function is a type of mathematical function that has abrupt changes or breaks in its graph. This means that the function is not defined for certain values within its domain and has a disjointed or interrupted curve. In other words, if you were to draw the graph of a discontinuous function without lifting your pencil, it would not be a single, continuous line.
How do you determine if a function is continuous or discontinuous?
To determine if a function is continuous or discontinuous, you can use the following criteria:
- A function is continuous if it is defined for all values within its domain and has a smooth, unbroken curve.
- A function is discontinuous if it is not defined for certain values within its domain and has a disjointed or interrupted curve.
- You can also use the concept of limits to determine if a function is continuous or discontinuous at a specific point. A function is continuous at a point if the limit of the function as x approaches that point is equal to the value of the function at that point.
What is a piece-wise function?
A piece-wise function is a type of mathematical function that is defined by different equations for different intervals or pieces of its domain. This means that the function has different rules or formulas that apply to different parts of its domain. For example, a piece-wise function may have one equation for values less than 5, and a different equation for values greater than or equal to 5.
How do you graph a piece-wise function?
To graph a piece-wise function, you can follow these steps:
- Determine the different intervals or pieces of the function's domain and the corresponding equations for each piece.
- Plot points for each piece of the function, using the corresponding equation.
- Connect the points for each piece with a line or curve.
- Make sure to indicate any breaks or discontinuities in the graph.