Special Functions
Objective: Write and graph piecewise and absolute value
functions.
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
Example 1
Example 1
Try This
• Graph:
4
12)(
x
xxf
51 if
12- if
x
x
Try This
• Graph:
-2x + 1 x y -2 5 1 -1
4
12)(
x
xxf
51 if
12- if
x
x
Try This
• Graph:
4
12)(
x
xxf
51 if
12- if
x
x
Try This
• Graph:
x – 4 x y 1 -3 5 1
4
12)(
x
xxf
51 if
12- if
x
x
Try This
• Graph:
4
12)(
x
xxf
51 if
12- if
x
x
Try This
Try This
Try This
Try This
Writing Equations
• Write the piecewise function represented by the graph below.
Writing Equations
• Write the piecewise function represented by the graph below.
Writing Equations
• Write the piecewise function represented by the graph below.
Writing Equations
• Write the piecewise function represented by the graph below.
Absolute Value
• The absolute value function, denoted by f(x) = |x|, can be defined as a piecewise function as follows:
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
Example 4
Example 4
Example 4
Homework
• Page 129• 17-27 odd• 58, 59