Special Functions Objective: Write and graph piecewise and absolute value functions.
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Transcript of Special Functions Objective: Write and graph piecewise and absolute value functions.
![Page 1: Special Functions Objective: Write and graph piecewise and absolute value functions.](https://reader033.fdocuments.us/reader033/viewer/2022061305/5513fab3550346e7488b45ec/html5/thumbnails/1.jpg)
Special Functions
Objective: Write and graph piecewise and absolute value
functions.
![Page 2: Special Functions Objective: Write and graph piecewise and absolute value functions.](https://reader033.fdocuments.us/reader033/viewer/2022061305/5513fab3550346e7488b45ec/html5/thumbnails/2.jpg)
Piecewise Functions
• A truck driver earns $21.00 per hour for the first 40 hours worked in one week. The driver earns time-and-a-half, or $31.50 , for each hour worked in excess of 40. The pair of function rules below represent the drivers wage, w(h), as a function of the hours worked in one week, h.
42050.31
21)(
h
hhw
40 if
400 if
h
h
![Page 3: Special Functions Objective: Write and graph piecewise and absolute value functions.](https://reader033.fdocuments.us/reader033/viewer/2022061305/5513fab3550346e7488b45ec/html5/thumbnails/3.jpg)
Example 1
![Page 4: Special Functions Objective: Write and graph piecewise and absolute value functions.](https://reader033.fdocuments.us/reader033/viewer/2022061305/5513fab3550346e7488b45ec/html5/thumbnails/4.jpg)
Example 1
![Page 5: Special Functions Objective: Write and graph piecewise and absolute value functions.](https://reader033.fdocuments.us/reader033/viewer/2022061305/5513fab3550346e7488b45ec/html5/thumbnails/5.jpg)
Try This
• Graph:
4
12)(
x
xxf
51 if
12- if
x
x
![Page 6: Special Functions Objective: Write and graph piecewise and absolute value functions.](https://reader033.fdocuments.us/reader033/viewer/2022061305/5513fab3550346e7488b45ec/html5/thumbnails/6.jpg)
Try This
• Graph:
-2x + 1 x y -2 5 1 -1
4
12)(
x
xxf
51 if
12- if
x
x
![Page 7: Special Functions Objective: Write and graph piecewise and absolute value functions.](https://reader033.fdocuments.us/reader033/viewer/2022061305/5513fab3550346e7488b45ec/html5/thumbnails/7.jpg)
Try This
• Graph:
4
12)(
x
xxf
51 if
12- if
x
x
![Page 8: Special Functions Objective: Write and graph piecewise and absolute value functions.](https://reader033.fdocuments.us/reader033/viewer/2022061305/5513fab3550346e7488b45ec/html5/thumbnails/8.jpg)
Try This
• Graph:
x – 4 x y 1 -3 5 1
4
12)(
x
xxf
51 if
12- if
x
x
![Page 9: Special Functions Objective: Write and graph piecewise and absolute value functions.](https://reader033.fdocuments.us/reader033/viewer/2022061305/5513fab3550346e7488b45ec/html5/thumbnails/9.jpg)
Try This
• Graph:
4
12)(
x
xxf
51 if
12- if
x
x
![Page 10: Special Functions Objective: Write and graph piecewise and absolute value functions.](https://reader033.fdocuments.us/reader033/viewer/2022061305/5513fab3550346e7488b45ec/html5/thumbnails/10.jpg)
Try This
![Page 11: Special Functions Objective: Write and graph piecewise and absolute value functions.](https://reader033.fdocuments.us/reader033/viewer/2022061305/5513fab3550346e7488b45ec/html5/thumbnails/11.jpg)
Try This
![Page 12: Special Functions Objective: Write and graph piecewise and absolute value functions.](https://reader033.fdocuments.us/reader033/viewer/2022061305/5513fab3550346e7488b45ec/html5/thumbnails/12.jpg)
Try This
![Page 13: Special Functions Objective: Write and graph piecewise and absolute value functions.](https://reader033.fdocuments.us/reader033/viewer/2022061305/5513fab3550346e7488b45ec/html5/thumbnails/13.jpg)
Try This
![Page 14: Special Functions Objective: Write and graph piecewise and absolute value functions.](https://reader033.fdocuments.us/reader033/viewer/2022061305/5513fab3550346e7488b45ec/html5/thumbnails/14.jpg)
Writing Equations
• Write the piecewise function represented by the graph below.
![Page 15: Special Functions Objective: Write and graph piecewise and absolute value functions.](https://reader033.fdocuments.us/reader033/viewer/2022061305/5513fab3550346e7488b45ec/html5/thumbnails/15.jpg)
Writing Equations
• Write the piecewise function represented by the graph below.
![Page 16: Special Functions Objective: Write and graph piecewise and absolute value functions.](https://reader033.fdocuments.us/reader033/viewer/2022061305/5513fab3550346e7488b45ec/html5/thumbnails/16.jpg)
Writing Equations
• Write the piecewise function represented by the graph below.
![Page 17: Special Functions Objective: Write and graph piecewise and absolute value functions.](https://reader033.fdocuments.us/reader033/viewer/2022061305/5513fab3550346e7488b45ec/html5/thumbnails/17.jpg)
Writing Equations
• Write the piecewise function represented by the graph below.
![Page 18: Special Functions Objective: Write and graph piecewise and absolute value functions.](https://reader033.fdocuments.us/reader033/viewer/2022061305/5513fab3550346e7488b45ec/html5/thumbnails/18.jpg)
Absolute Value
• The absolute value function, denoted by f(x) = |x|, can be defined as a piecewise function as follows:
![Page 19: Special Functions Objective: Write and graph piecewise and absolute value functions.](https://reader033.fdocuments.us/reader033/viewer/2022061305/5513fab3550346e7488b45ec/html5/thumbnails/19.jpg)
Absolute Value
• The absolute value function, denoted by f(x) = |x|, can be defined as a piecewise function as follows:
xx
xxxf
||
||)(
0 if
0 if
x
x
![Page 20: Special Functions Objective: Write and graph piecewise and absolute value functions.](https://reader033.fdocuments.us/reader033/viewer/2022061305/5513fab3550346e7488b45ec/html5/thumbnails/20.jpg)
Example 4
![Page 21: Special Functions Objective: Write and graph piecewise and absolute value functions.](https://reader033.fdocuments.us/reader033/viewer/2022061305/5513fab3550346e7488b45ec/html5/thumbnails/21.jpg)
Example 4
![Page 22: Special Functions Objective: Write and graph piecewise and absolute value functions.](https://reader033.fdocuments.us/reader033/viewer/2022061305/5513fab3550346e7488b45ec/html5/thumbnails/22.jpg)
Example 4
![Page 23: Special Functions Objective: Write and graph piecewise and absolute value functions.](https://reader033.fdocuments.us/reader033/viewer/2022061305/5513fab3550346e7488b45ec/html5/thumbnails/23.jpg)
![Page 24: Special Functions Objective: Write and graph piecewise and absolute value functions.](https://reader033.fdocuments.us/reader033/viewer/2022061305/5513fab3550346e7488b45ec/html5/thumbnails/24.jpg)
![Page 25: Special Functions Objective: Write and graph piecewise and absolute value functions.](https://reader033.fdocuments.us/reader033/viewer/2022061305/5513fab3550346e7488b45ec/html5/thumbnails/25.jpg)
![Page 26: Special Functions Objective: Write and graph piecewise and absolute value functions.](https://reader033.fdocuments.us/reader033/viewer/2022061305/5513fab3550346e7488b45ec/html5/thumbnails/26.jpg)
Homework
• Page 129• 17-27 odd• 58, 59