2.7 – Use of Absolute Value Functions and Transformations.
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Transcript of 2.7 – Use of Absolute Value Functions and Transformations.
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2.7 – Use of Absolute Value Functions and Transformations
![Page 2: 2.7 – Use of Absolute Value Functions and Transformations.](https://reader036.fdocuments.us/reader036/viewer/2022081810/5a4d1b5f7f8b9ab0599ac917/html5/thumbnails/2.jpg)
2.7 – Use of Absolute Value Functions and Transformations
• A transformation changes a graph’s size , shape, position, or orientation.
• A translation is a transformation that shifts a graph horizontally and/or vertically, but
does not change its size, shape, or orientation.
![Page 3: 2.7 – Use of Absolute Value Functions and Transformations.](https://reader036.fdocuments.us/reader036/viewer/2022081810/5a4d1b5f7f8b9ab0599ac917/html5/thumbnails/3.jpg)
2.7 – Use of Absolute Value Functions and Transformations
• The graph of y = |x – h| + k is the graph of y = |x| translated h units horizontally and k
units vertically.
•The vertex would be (h, k)
![Page 4: 2.7 – Use of Absolute Value Functions and Transformations.](https://reader036.fdocuments.us/reader036/viewer/2022081810/5a4d1b5f7f8b9ab0599ac917/html5/thumbnails/4.jpg)
2.7 – Use of Absolute Value Functions and Transformations
![Page 5: 2.7 – Use of Absolute Value Functions and Transformations.](https://reader036.fdocuments.us/reader036/viewer/2022081810/5a4d1b5f7f8b9ab0599ac917/html5/thumbnails/5.jpg)
2.7 – Use of Absolute Value Functions and TransformationsWhen a = -1, the graph of y = a|x| is a
reflection in the x-axis of the graph of y = |x|. When a < 0, but a doesn’t equal -1, the graph of y = a|x| is a vertical stretch or shrink with a reflection in the x-axis of the graph of y = |x|.
![Page 6: 2.7 – Use of Absolute Value Functions and Transformations.](https://reader036.fdocuments.us/reader036/viewer/2022081810/5a4d1b5f7f8b9ab0599ac917/html5/thumbnails/6.jpg)
2.7 – Use of Absolute Value Functions and Transformations
Example :Graph the function and compare the graph
with the graph of y = |x|:• y = |x -2| + 5
• Y = ¼|x|• f(x) = -3|x + 1| - 2
![Page 7: 2.7 – Use of Absolute Value Functions and Transformations.](https://reader036.fdocuments.us/reader036/viewer/2022081810/5a4d1b5f7f8b9ab0599ac917/html5/thumbnails/7.jpg)
2.7 – Use of Absolute Value Functions and TransformationsTransformations of General Graphs
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2.7 – Use of Absolute Value Functions and Transformations
Example: The graph of a function y = f(x) is
shown. Sketch the graph of the given function.
a. y = 2f(x)b. y = -f(x + 2) + 1c. y = .5f(x)d. y = 2f(x – 3) – 1