u2 l2 one to one functions and transformations.notebook · u2 l2 one to one functions and...
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U2 L2 One to One Functions and Transformations.notebook
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October 26, 2016
Oct 238:34 AM
HW answers
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U2 L2 One to One Functions and Transformations.notebook
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October 26, 2016
Oct 238:35 AM
![Page 3: U2 L2 One to One Functions and Transformations.notebook · U2 L2 One to One Functions and Transformations.notebook 4 October 26, 2016 Oct 52:09 PM A Function is a correspondence between](https://reader031.vdocument.in/reader031/viewer/2022021901/5b8457187f8b9aea498c1d4b/html5/thumbnails/3.jpg)
U2 L2 One to One Functions and Transformations.notebook
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October 26, 2016
Oct 52:04 PM
U2 Lesson 2
One to One Functions
and
Transformations
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U2 L2 One to One Functions and Transformations.notebook
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October 26, 2016
Oct 52:09 PM
A Function is a correspondence between two sets A and B IF AND ONLY IF each member of A corresponds to one and only one member of B. (every x has exactly one y)
Recall that last year we said that functions have UNIQUE x's.
Those UNIQUE x's represent the DOMAIN of the function, and the obtained y's are the RANGE.
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U2 L2 One to One Functions and Transformations.notebook
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October 26, 2016
Oct 268:05 AM
One of the following graphs shows a relationship where y is a function of x and one does not.
Vertical Line Test: A graph is a function if and only if NO vertical line intersects the graph of the relation at more than one point.
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U2 L2 One to One Functions and Transformations.notebook
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October 26, 2016
Oct 52:18 PM
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U2 L2 One to One Functions and Transformations.notebook
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Oct 52:22 PM
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U2 L2 One to One Functions and Transformations.notebook
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October 26, 2016
Oct 52:23 PM
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U2 L2 One to One Functions and Transformations.notebook
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October 26, 2016
Oct 52:24 PM
A correspondence between a preimage and its image is a Mapping if and only if each preimage corresponds to one and only one image.
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U2 L2 One to One Functions and Transformations.notebook
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October 26, 2016
Oct 52:34 PM
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U2 L2 One to One Functions and Transformations.notebook
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October 26, 2016
Oct 52:36 PM
Many mappings are NOT useful.... We don't want to start with a triangle and end up with a segment or a point.
We want to have mappings that Preserve the number of preimage and image points.
In Algebra, functions that did this were called OnetoOne Functions. In Geometry, functions that do this are called Transformations.OnetoOne FunctionA function for which every element of the range of the function corresponds to exactly one element of the domain. Onetoone is often written 11
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U2 L2 One to One Functions and Transformations.notebook
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October 26, 2016
Oct 268:13 AM
Horizontal Line TestA test use to determine if a function is onetoone. If a horizontal line intersects a function's graph more than once, then the function is not onetoone.
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U2 L2 One to One Functions and Transformations.notebook
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October 26, 2016
Oct 52:44 PM
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U2 L2 One to One Functions and Transformations.notebook
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October 26, 2016
Oct 52:50 PM
U2 Lesson 2
Homework
online