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