Lesson 1-7

Example 1
Graph .

First, graph the constant function for . This graph is part of a horizontal line. Because the point at (-1, 3) is included in the graph, draw a closed circle at that point.

Second, graph the function  for	
. Because  is not included
in this part of the domain, draw an open circle
at (-1, 5). is included in the domain, so
draw a closed circle at (4, 0) since for
.

Third, graph the line  for .
Draw an open circle at (4, 2) since for
.

Example 2
Graph .

Make a table of values. The domain values will be intervals for which the greatest integer function will be evaluated.

x	f(x)		
-3  x < -2	6		
-2  x < -1	4		
-1  x < 0	2		
0  x < 1	0		
1  x < 2	-2		
2  x < 3	-4		
3  x < 4	-6		
4  x < 5	-8		

Notice that the domain for this greatest integer function is all real numbers and the range is even integers.

Example 3
POSTAGE  The amount of postage a person has to pay in order to mail a parcel via first class mail depends upon the weight of the parcel. The table shows the cost of postage for each of the weight classes up to 6 ounces.

a.	Graph the cost postage for the different parcel weights.

b.	What is the cost of postage for a parcel that weighs 4.2 ounces?
	First-Class Mail
Postage Rates	
	Weight (ounces)	Cost of Postage ($)	
	0 < x  1	0.37	
	1 < x  2	0.60	
	2 < x  3	0.83	
	3 < x  4	1.06	
	4 < x  5	1.29	
	5 < x  6	1.52	

a.		b.	4.2 ounces falls in the interval 4 ounces to 5 ounces. Thus, the cost of a parcel weighing 4.2 ounces is $1.29.	

Example 4
Graph f(x) = |x| + 1.

Use a table of values to determine points on the graph.

x	|x| + 1	(x, f(x))		
-4	3	(-4, 3) 		
-2	2	(-2, 2) 		
0	1	(0, 1) 		
2	2	(2, 2) 		
4	3	(4, 3) 		
6	4	(6, 4) 		

Example 5
Identify the type of function that models each situation. Then write a function
for the situation.

a.	The acceptable temperature range to store refrigerated foods is between 34F and 40F. Therefore, the temperature of a refrigerator may be within a 3-degree range of 37F. Outside of this range, and food either begins to freeze or spoil.

The situation can be represented with an absolute value function. Let t represent the temperature and d(t) represent the discrepancy. Then .
		
b.	A credit card company is running a rewards program in which its card members earn one reward point for every dollar they spend using their credit card. Points are only awarded in whole number increments for each whole dollar spent. Therefore, if a person spends $1.00 using her card, she earns 1 reward point, but if she spends $1.70, she will still only earn 1 reward point.

This can be described by a greatest integer function.

Let d represent the number of dollars spent and  represent the points earned.