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Visualizing Method |
Description |
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have the benefit of showing both the input space and the output space at once, but as a result, they are highly limited by dimension. For this reason, they are only really useful for single-variable functions and multivariable functions with a two-dimensional input and a one-dimensional output | |
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Contour maps only show the input space and are useful for functions with a two-dimensional input and a one-dimensional output | |
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Parametric curves and surfaces only show the output space and are used for functions whose output space has more dimensions than the input space | |
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Scalar Fields |
These apply to functions whose input space and output space have the same number of dimensions. For example, functions with two-dimensional inputs and two-dimensional outputs, or three-dimensional inputs and three-dimensional outputs can be used with vector fields |
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These have the benefit of applying to any function, no matter the dimension of the input and output space. However, the downside is that they can only be represented using an animation or a schematic drawing. As such, they are most useful for gaining a conceptual understanding of what a function is doing, but are impractical for representing the function precisely |