Discrete & Continuous Domains

Holt Course 3 3.3Glencoe 2-3C

Adults $4.00

Children $2.00

8-2xyor 1624 yx

Domain (x-values): 0, 1, 2, 3, 4Range (y-values): 8, 6, 4, 2, 0

• The domain is discrete because it has only the numbers 0, 1, 2, 3, and 4. Discrete graphs are made up of distinct, or unconnected, points.• Since there is no such thing as half a ticket, or one-forth of a ticket the domain does not include those points between the points graphed.

Functions shows a recipes mix of adult & children show tickets.

8-2xyor 1624 yxDomain (x-values): x ≥ 0 and x ≤ 0

(all numbers from 0 to 4)Range (y-values): y ≥ 0 and y ≤ 8

(all numbers from 0 to 8)

• The domain is continuous because it includes all numbers from 0 to 4 on the number line. Continuous graphs are made up connected lines or curves. • Cheese can be divided into fractions or decimals, so it is shown to be continuous by using a line to include all of those points.

Cheddar: $2/lb

Swiss: $4/lb

Functions shows a recipes mix of cheddar & Swiss cheese.

•Write a linear function to represent each problem.•Graph the function.•Describe the domain and range of each function. Is the domain discrete or continuous?

You are in charge of reserving hotel rooms for a baseball team. Each room costs $69, plus $6 tax, per night. You need each room for two night. You need 10 to 16 rooms. Write a function for the total hotel costs.

yx 150

1500)10(150 1650)11(150 1800)12(150 1950)13(150

1050)14(150

2250)15(150 2400)16(150

Discrete

•Write a linear function to represent each problem.•Graph the function.•Describe the domain and range of each function. Is the domain discrete or continuous?

The airline you are using for the baseball trip needs an estimate of the total weight of the team’s luggage. You determine that there will be 36 pieces of luggage and each piece will weigh from 25 to 45 pounds. Write a function for the total weight of the luggage.

1620 or x 4536x

900or x 2536

x

1620 x

900 x

Continuous

Key Idea• A discrete domain is a set of input values that consists

of only certain numbers in an interval. Like integers 1 to 4.

• A continuous domain is a set of input values that consists of all numbers in an interval. Like all numbers 1 to 4.

BACK

-3 -2 -1 0 1 2 3 4 5

-3 -2 -1 0 1 2 3 4 5

The graphs show the speeds of two cars over time. Tell which graph corresponds to each situation.

Matching Situations to Graphs

Mr. Lee is traveling on the highway. He pulls over, stops, then accelerates rapidly as he gets back on the highway. Graph 2

The graphs show the speeds of two cars over time. Tell which graph corresponds to each situation.

Matching Situations to Graphs

Ms. Montoni slows down as she leaves the main road. She continues to slow down as she turns onto other streets and eventually stops in front of her house. Graph 1

Check It Out: Example 1A

Tell which graph corresponds to the situation described below.

Time

Run

ner’

s Sp

eed

Time

Run

ner’

s Sp

eed

Time

Run

ner’

s Sp

eedGraph 1 Graph 2 Graph 3

Jamie begins the race, and soon feels a pain in a muscle. He is unable to complete the race.

Graph 2—Jamie is unable to complete the race, so his speed decreases to zero.

Check It Out: Example 1B

Tell which graph corresponds to the situation described below.

Time

Run

ner’

s Sp

eed

Time

Run

ner’

s Sp

eed

Time

Run

ner’

s Sp

eedGraph 1 Graph 2 Graph 3

Melissa builds up her speed during the beginning of the race. She maintains her running speed for the remainder of the race.

Graph 1—Melissa’s speed increases at the beginning and then the graph remains constant.

Create a graph for the situation. Tell whether the graph is continuous or discrete.

The table showsthe temperatureinside a car over time.

Time 8:00 8:30 12:00 12:30Temp.(F) 71 71 82 74

Car Temperature

6466687072747678808284

8:00 8:30 12:00 12:30

Time

Tem

p (

F)

Creating a Graph of a Situation

Since every value of time has a corresponding altitude, connect the points.

The graph is continuous.

Create a graph for the situation. Tell whether the graph is continuous or discrete.

A market sells pumpkins for $5 each.

Pumpkin Cost

0

5

10

15

20

25

30

35

40

0 2 4 6 8

Pumpkins Purchased

Cost(

$)

Creating a Graph of a Situation

The cost (y-axis) increases by $5 for each pumpkin purchased (x-axis).

Because each person can only buy whole pumpkins or none at all, the graph is distinct points.

The graph is discrete.

Create a graph for the situation. Tell whether the graph is continuous or discrete.

The table showsthe distance traveled during a family vacation.

Distance Travelled

Example 2A

Since every value of time has a corresponding altitude, connect the points.

The graph is continuous.

Time 8:00 10:00 12:00 2:00Distance (mi) 280 320 500 580

0

100

200

300

400

500

600

700

8:00 10:00 12:00 2:00

Time

Dis

tan

ce (

mi)

Lesson Quiz

Tell which graph corresponds to the situation. Then tell whether the graph is continuous or discrete.

A bus pulls out from the gas station. It drives to its first stop. Then the bus gets on the expressway.

Graph B; continuous

1. Maggi has $25 in her bank account. She gets $5 every day from her father and deposits the money in the account for the first three days. On the fourth day, she buys a hat for herself with the money. Identify the table that corresponds to this situation.

A. B.

Lesson Quiz for Student Response Systems

Discrete & Continuous Domains

Holt Course 3 3.3Glencoe 2-3C