Dr. Byrne
Fall 2010
Math 112
Worksheet 2.1: Increasing and Decreasing Intervals, Minima and Maxima
Determine the intervals in which the function is increasing or decreasing.
Find any relative maxima or minima.
Over which intervals
(a) is the function increasing?
(b) is the function decreasing?
What are the relative maxima?
What are the relative minima?
Worksheet 2.1: Piecewise Functions
Graphing a piecewise function.
The following function is
The following function is
defined piecewise:
defined piecewise:
 2,

f ( x)   1,
 3,

for x  2,
for 2  x  4,
for x  4.
3,
f ( x)  
1,
for x  1
for x  1
Graph the function:
Graph the function:
The following function is
defined piecewise:
2,
f ( x)  
4,
for x  4
for x  4
Graph the function:
Describe the following graph as a piecewise function:
Find specified values and make a hand-drawn graph of the piecewise function.
 x  4,
g ( x)  
8  x,
for x  1 2. Graph the function.
for x  1
x
-4
0
1
3
1. Find the function values:
g (4) 
g ( 0) 
g (1) 
g (3) 
y
Worksheet 2.1: Applications
Adoption Area. Petsmart has 14 feet of fence with which to make a rectangular pen to hold
puppies for adoption. Suppose that the rectangle is x feet wide.
(a) Express the area of the pen A as a
function of x.
x
A
(b) What is the domain of the function?
(c) Graph the area A verses the width of
the pen.
(d) What width maximizes the area if the fence
breaks up into 1-foot pieces?