Absolute Value as Piecewise Functions Lesson2.5. Example f (x) = x + 1, if x < 1 2, if 1 x 3 (x-3) 2...
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Transcript of Absolute Value as Piecewise Functions Lesson2.5. Example f (x) = x + 1, if x < 1 2, if 1 x 3 (x-3) 2...
![Page 1: Absolute Value as Piecewise Functions Lesson2.5. Example f (x) = x + 1, if x < 1 2, if 1 x 3 (x-3) 2 + 2, if x > 3.](https://reader033.fdocuments.us/reader033/viewer/2022061305/55145551550346494e8b5329/html5/thumbnails/1.jpg)
Absolute Value as Piecewise Functions
Lesson2.5Lesson2.5
![Page 2: Absolute Value as Piecewise Functions Lesson2.5. Example f (x) = x + 1, if x < 1 2, if 1 x 3 (x-3) 2 + 2, if x > 3.](https://reader033.fdocuments.us/reader033/viewer/2022061305/55145551550346494e8b5329/html5/thumbnails/2.jpg)
Example
f (x) =
x + 1, if x < 1
2, if 1 ≤ x ≤ 3
(x-3)2 + 2, if x > 3
![Page 3: Absolute Value as Piecewise Functions Lesson2.5. Example f (x) = x + 1, if x < 1 2, if 1 x 3 (x-3) 2 + 2, if x > 3.](https://reader033.fdocuments.us/reader033/viewer/2022061305/55145551550346494e8b5329/html5/thumbnails/3.jpg)
Absolute Value as Piecewise
We usually write an absolute value function as f (x)= x , but since absolute value is a measure of distance and distance is always positive, it also can be written as follows:
f (x) = -x, if x < 0
x, if x ≥ 0
![Page 4: Absolute Value as Piecewise Functions Lesson2.5. Example f (x) = x + 1, if x < 1 2, if 1 x 3 (x-3) 2 + 2, if x > 3.](https://reader033.fdocuments.us/reader033/viewer/2022061305/55145551550346494e8b5329/html5/thumbnails/4.jpg)
Writing Abs. Value as Piecewise
To identify the number in the domain, set x – h = 0 and solve for x.
For I x - h I ≥ 0, simplify the equation given by distributing and combining like terms.
For I x - h I < 0, substitute –(x - h) in place of I x - h I. Then, simplify the equation given by distributing and combining like terms.
![Page 5: Absolute Value as Piecewise Functions Lesson2.5. Example f (x) = x + 1, if x < 1 2, if 1 x 3 (x-3) 2 + 2, if x > 3.](https://reader033.fdocuments.us/reader033/viewer/2022061305/55145551550346494e8b5329/html5/thumbnails/5.jpg)
Example:
Write y = 2 Ix – 4I – 10 as a piecewise function.
Use 4 in your domain.
For (x-4) ≥ 0
2(x – 4) – 10 = 2x – 8 – 10 = 2x – 18 (when x ≥ 4)
For (x-4) < 0
2[-(x-4)] – 10 = 2(-x + 4) – 10 = -2x + 8 – 10
= -2x – 2 (when x < 4))
![Page 6: Absolute Value as Piecewise Functions Lesson2.5. Example f (x) = x + 1, if x < 1 2, if 1 x 3 (x-3) 2 + 2, if x > 3.](https://reader033.fdocuments.us/reader033/viewer/2022061305/55145551550346494e8b5329/html5/thumbnails/6.jpg)
More Examples:
Write y = 2 Ix – 4I – 10 as a piecewise function.
For (x-4) ≥ 0
2(x – 4) – 10 = 2x – 8 – 10 = 2x – 18 (when x ≥ 4)
For (x-4) < 0
2[-(x-4)] – 10 = 2(-x + 4) – 10 = -2x + 8 – 10
= -2x – 2 (when x < 4))
![Page 7: Absolute Value as Piecewise Functions Lesson2.5. Example f (x) = x + 1, if x < 1 2, if 1 x 3 (x-3) 2 + 2, if x > 3.](https://reader033.fdocuments.us/reader033/viewer/2022061305/55145551550346494e8b5329/html5/thumbnails/7.jpg)
Graphs of Both
y=2x-18y=-2x-2
![Page 8: Absolute Value as Piecewise Functions Lesson2.5. Example f (x) = x + 1, if x < 1 2, if 1 x 3 (x-3) 2 + 2, if x > 3.](https://reader033.fdocuments.us/reader033/viewer/2022061305/55145551550346494e8b5329/html5/thumbnails/8.jpg)
EOCT Practice
A
![Page 9: Absolute Value as Piecewise Functions Lesson2.5. Example f (x) = x + 1, if x < 1 2, if 1 x 3 (x-3) 2 + 2, if x > 3.](https://reader033.fdocuments.us/reader033/viewer/2022061305/55145551550346494e8b5329/html5/thumbnails/9.jpg)
EOCT Practice
C
![Page 10: Absolute Value as Piecewise Functions Lesson2.5. Example f (x) = x + 1, if x < 1 2, if 1 x 3 (x-3) 2 + 2, if x > 3.](https://reader033.fdocuments.us/reader033/viewer/2022061305/55145551550346494e8b5329/html5/thumbnails/10.jpg)
Writing Abs. Value as Piecewise
Using a graph
![Page 11: Absolute Value as Piecewise Functions Lesson2.5. Example f (x) = x + 1, if x < 1 2, if 1 x 3 (x-3) 2 + 2, if x > 3.](https://reader033.fdocuments.us/reader033/viewer/2022061305/55145551550346494e8b5329/html5/thumbnails/11.jpg)
Writing Abs. Value as Piecewise
Try this one...