discrete & continuous domains - math 10
TRANSCRIPT
2. discrete and Continious.notebook
1
November 03, 2014
Discrete & Continuous Domains
2. discrete and Continious.notebook
2
November 03, 2014
• Discrete functions consist of points that are not connected.
• Continuous functions can be graphed with a line or smooth curve and contain an infinite number of points.
2. discrete and Continious.notebook
3
November 03, 2014
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
2. discrete and Continious.notebook
4
November 03, 2014
Adults $4.00Children $2.00
• 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.
Domain (x‐values): 0, 1, 2, 3, 4Range (y‐values): 8, 6, 4, 2, 0
2. discrete and Continious.notebook
5
November 03, 2014
Domain (x‐values): x ≥ 0 and x ≤ 4(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 of 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.
2. discrete and Continious.notebook
6
November 03, 2014
• 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.
(69 + 6) x 2 =
2. discrete and Continious.notebook
7
November 03, 2014
x Y
150(14) = 2100
2. discrete and Continious.notebook
8
November 03, 2014
Discrete
2. discrete and Continious.notebook
9
November 03, 2014
• Write a linear function to represent each problem.• Graph the 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.
2. discrete and Continious.notebook
10
November 03, 2014
Continuous
2. discrete and Continious.notebook
11
November 03, 2014
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
2. discrete and Continious.notebook
12
November 03, 2014
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
2. discrete and Continious.notebook
13
November 03, 2014