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