File:Function image and preimage 3.png
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Function_image_and_preimage_3.png (646 × 399 pixels, file size: 71 KB, MIME type: image/png)
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This diagram image could be re-created using vector graphics as an SVG file. This has several advantages; see Commons:Media for cleanup for more information. If an SVG form of this image is available, please upload it and afterwards replace this template with
{{vector version available|new image name}}.
It is recommended to name the SVG file “Function image and preimage 3.svg”—then the template Vector version available (or Vva) does not need the new image name parameter. |
Summary
| Description |
English: Illustration of y=(x-1)*(x-3)*(x-5) with preimage gotten from y = [1,2.5] and image from x = [3.50, 4.25], with arrows.
(This is the graph of the function "f(x) = x<sup>3</sup> − 9x<sup>2</sup> + 23x − 15" when written in unfactored form.)
The interval A = [3.5, 4.25] is a subset of the domain, thus it is shown as part of the x-axis (green). The image of A is (approximately) the interval [−3.08, −1.88]. It is obtained by projecting to the y-axis (along the blue arrows) the intersection of the graph with the light green area consisting of all points whose x-coordinate is between 3.5 and 4.25, the part of the (vertical) y-axis shown in blue.
The preimage of B = [1, 2.5] consists of three intervals. They are obtained by projecting the intersection of the light red area with the graph to the x-axis. |
| Date | |
| Source | Graph derived from Excel and artwork added via Autodesk Sketchbook Pro |
| Author | Wvbailey |
- Other information
Added arrows to indicate "flow", perhaps will help student
Licensing
I, the copyright holder of this work, hereby publish it under the following licenses:
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Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License. |
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 15:01, 3 August 2012 | | 646 × 399 (71 KB) | wikimediacommons>Wvbailey | Reverted to version as of 12:55, 3 August 2012 |
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