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A piece-wise continuous function is one which has a domain that is broken up inot sub-domains. Over each sub-domain the function is continuous but at the end of the domain one of the following possibilities can occur:
- the domain itself is discontinuous (disjoint domains),
- the value of the function is not defined at the start or end-point of the domain ((a hole),
- the value of the function at the end point of a sub-domain is different to its value at the start of the next sub-domain (a step-discontinuity).
A piece-wise continuous function is one which has a domain that is broken up inot sub-domains. Over each sub-domain the function is continuous but at the end of the domain one of the following possibilities can occur:
- the domain itself is discontinuous (disjoint domains),
- the value of the function is not defined at the start or end-point of the domain ((a hole),
- the value of the function at the end point of a sub-domain is different to its value at the start of the next sub-domain (a step-discontinuity).
A piece-wise continuous function is one which has a domain that is broken up inot sub-domains. Over each sub-domain the function is continuous but at the end of the domain one of the following possibilities can occur:
- the domain itself is discontinuous (disjoint domains),
- the value of the function is not defined at the start or end-point of the domain ((a hole),
- the value of the function at the end point of a sub-domain is different to its value at the start of the next sub-domain (a step-discontinuity).
A piece-wise continuous function is one which has a domain that is broken up inot sub-domains. Over each sub-domain the function is continuous but at the end of the domain one of the following possibilities can occur:
- the domain itself is discontinuous (disjoint domains),
- the value of the function is not defined at the start or end-point of the domain ((a hole),
- the value of the function at the end point of a sub-domain is different to its value at the start of the next sub-domain (a step-discontinuity).
Wiki User
∙ 11y ago
Wiki User
∙ 11y agoA piece-wise continuous function is one which has a domain that is broken up inot sub-domains. Over each sub-domain the function is continuous but at the end of the domain one of the following possibilities can occur:
- the domain itself is discontinuous (disjoint domains),
- the value of the function is not defined at the start or end-point of the domain ((a hole),
- the value of the function at the end point of a sub-domain is different to its value at the start of the next sub-domain (a step-discontinuity).
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Both the Greatest Integer Function and the Absolute Value Function are considered Piece-Wise Defined Functions. This implies that the function was put together using parts from other functions.
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What is a piece-wise function?
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What is a nonlinear function in which the variable is in the exponent?
Maybe possibly a piece-wise function...
The greatest integer function and absolute value function are both examples of functions that can be defined as what?
Both the Greatest Integer Function and the Absolute Value Function are considered Piece-Wise Defined Functions. This implies that the function was put together using parts from other functions.
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That means that the functions is made up of different functions - for example, one function for one interval, and another function for a different interval. Such a function is still a legal function - it meets all the requirements of the definition of a "function". However, in the general case, you can't write it as "y = (some expression)", using a single expression at the right.
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Well, firstly, the derivative of a function simply refers to slope. Usually we say that the function is not differentiable at a point.Say you have a function such as this:f(x)=|x|Another way to represent that would be as a piece-wise function:g(x) = { -x for x= 0The problem arises at the specific point x=0. If you look at the slope--the change in the function--from the left and right of x, you notice that it is different, negative 1 and positive 1. So, we can say that the function is not differentiable at x=0 because of that sudden change.There are however, a few functions that are nowhere differentiable. One example is the Weirstrass function. The even more ironic thing about this function is that it is continuous everywhere! Since this function is not differentiable anywhere, many might call it a non-differentiable function.There are absolutely other examples.
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Piece wise functions can do everything. Take two pieces of two rational functions, one have a horizontal asymptote as x goes to -infinity and the other have a slanted (oblique) one as x goes to +infinity. It is still a rational function.
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The term "limit" in calculus describes what is occurring as a line approaches a specific point from either the left or right hand side. Some limits approach infinity while some approach specific points depending on the function given. If the function is a piece-wise function, the limit may not reach a specific value depending on the function given. For a more in-depth definition here is a good link to use: * http://www.math.hmc.edu/calculus/tutorials/limits/
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guarantees a wise and efficient use of the government resources for the development of a country.
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