2.6 Special Functions

Warm-up (IN)

Learning Objective: to write and graph piecewise and absolute value functions and to apply them to real world situations.

1. Graph the piecewise function.

64 if 54

1

42 if 4

20 if 2

xx

x

xx

xf

Notes

Learning Objective: to write and graph piecewise and absolute value functions and to apply them to real world situations.

Ex 1 – 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. Represent the situation using a piecewise function.

hourperwagehw hoursoh f #

hw

h21 400 if h

h5.31 420 40 if h

Need to take away the $420 he made on regular time

W2LWrite a different real world situation that can be represented using a piecewise function

Learning Objective: to write and graph piecewise and absolute value functions and to apply them to real world situations.

Ex 2 – Write the piecewise function represented in the graph.

if

if

if

xfx3 20 x

6 42 x10 x 64 x

Learning Objective: to write and graph piecewise and absolute value functions and to apply them to real world situations.

Absolute Value Function – xxf Can be represented with a piecewise function

xf

x 0 if x

x 0 if x

EX 3 – graph the function y x

1

-1

x y

0

2

0

2

1

1

2

-2

Learning Objective: to write and graph piecewise and absolute value functions and to apply them to real world situations.

EX 4 – graph the function and its inverse on the same coordinate plane.

1

-1

x y

0

2

2

8

5

5

8

-2

23 a. xxfinverse

1

-1

x y

0

2

2

8

5

5

8

-2

b. Try it! Pg. 127

HW – p. 129-132

#17-27 odd, 58-60, 73, 77-89 odd

Out – Is the inverse of a function? EXPLAIN!

Summary – I have a question about…

POW!!

xxf