Intermediate Algebra (11th edition)

The graph of a step function also may be shifted. For example, the graph of

is the same as the graph of shifted two units to the right. Similarly, the

graph of

is the graph of ƒ 1 x 2 shifted two units up.

g 1 x 2 = x + 2

ƒ 1 x 2 = x

h 1 x 2 = x- 2 

SECTION 11.1 Additional Graphs of Functions 639

x

y

• 5 – 4 – 3 – 2
  
  
  • 3
  
  
  • 4
  
  
  • 5
  
  
  
  

1

2

3

4

5

2534

f f (x) [[x]]

FIGURE 7

Greatest integer function

Domain:

Range:

(the set of integers)

5 Á, -3, -2, -1, 0, 1, 2, 3,Á 6

1 - q, q 2

ƒ 1 x 2 x

NOW TRY
EXERCISE 5
Graph Give
the domain and range.

ƒ 1 x 2 = x- 1 .

NOW TRY ANSWERS

5.

domain: ;

range: 5 Á, -2, -1, 0, 1, 2,Á 6

1 - q, q 2

1

0

y

x

23

f(x) = x – 1

–1

–3

–2

Applying a Greatest Integer Function

An overnight delivery service charges $25 for a package weighing up to 2 lb. For

each additional pound or fraction of a pound there is an additional charge of $3. Let

, or y, represent the cost to send a package weighing xpounds. Graph for x

in the interval

For xin the interval

For xin the interval

For xin the interval

For xin the interval

For xin the interval

The graph, which is that of a step function, is shown in FIGURE 8.

1 5, 6 4 , y= 34 + 3 =37.

1 4, 5 4 , y= 31 + 3 =34.

1 3, 4 4 , y= 28 + 3 =31.

1 2, 3 4 , y= 25 + 3 =28.

1 0, 2 4 , y= 25.

1 0, 6 4.

D 1 x 2 D 1 x 2

EXAMPLE 6

x

y

0 123456

10

20

30

40

Pounds

Dollars y = D(x)

FIGURE 8

NOW TRY
EXERCISE 6
The cost of parking a car at an
airport hourly parking lot is
$4 for the first hour and $2
for each additional hour or
fraction thereof. Let
the cost of parking a car for
xhours. Graph for xin
the interval 1 0, 5 4.

ƒ 1 x 2

ƒ 1 x 2 =

6.

4

2

6

10

8

0

y

x

12345

y = f(x)

NOW TRY

NOW TRY