How do we use graphs to represent real world relationships
This presentation is the property of its rightful owner.
Sponsored Links
1 / 15

How do we use graphs to represent real world relationships? PowerPoint PPT Presentation


  • 90 Views
  • Uploaded on
  • Presentation posted in: General

How do we use graphs to represent real world relationships?. Objectives. Match simple graphs with situations. Graph a relationship.

Download Presentation

How do we use graphs to represent real world relationships?

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


How do we use graphs to represent real world relationships

How do we use graphs to represent real world relationships?


How do we use graphs to represent real world relationships

Objectives

Match simple graphs with situations.

Graph a relationship.


How do we use graphs to represent real world relationships

Graphs can be used to illustrate many different situations. For example, trends shown on a cardiograph can help a doctor see how a patient’s heart is functioning.

To relate a graph to a given situation, use key words in the description.


How do we use graphs to represent real world relationships

Relating Graphs to Situations

Each day several leaves fall from a tree. One day a gust of wind blows off many leaves. Eventually, there are no more leaves on the tree. Choose the graph that best represents the situation.

Step 1 Read the graphs from left to right to show time passing.


How do we use graphs to represent real world relationships

Step 2 List key words in order and decide which graph shows them.

Never horizontal

Graph B

Slanting downward

rapidly

Graphs A, B, and C

Slanting downward until reaches zero

Graphs A, B, and C

Step 3 Pick the graph that shows all the key phrases in order.

The correct graph is B.


How do we use graphs to represent real world relationships

Example 1

The air temperature increased steadily for several hours and then remained constant. At the end of the day, the temperature increased slightly before dropping sharply. Choose the graph that best represents this situation.

Step 1 Read the graphs from left to right to show time passing .


How do we use graphs to represent real world relationships

Example 1 Continued

Step 2 List key words in order and decide which graph shows them.

Slanting upward

Graph C

Graphs A, B, and C

Horizontal

Slanting upward and then steeply downward

Graphs B and C

Step 3 Pick the graph that shows all the key phrases in order.

The correct graph is graph C.


How do we use graphs to represent real world relationships

As seen in Example 1, some graphs are connected lines or curves called continuous graphs. Some graphs are only distinct points. They are called discrete graphs

The graph on theme park attendance is an example of a discrete graph. It consists of distinct points because each year is distinct and people are counted in whole numbers only. The values between whole numbers are not included, since they have no meaning for the situation.


How do we use graphs to represent real world relationships

y

Speed

x

Time

Sketching Graphs for Situations

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

A truck driver enters a street, drives at a constant speed, stops at a light, and then continues.

As time passes during the trip (moving left to right along the x-axis) the truck's speed (y-axis) does the following:

• initially increases

• remains constant

• decreases to a stop

• increases

• remains constant

The graph is continuous.


How do we use graphs to represent real world relationships

Example 2:

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

A small bookstore sold between 5 and 8 books each day for 7 days.

The number of books sold (y-axis) varies for each day (x-axis).

Since the bookstore accounts for the number of books sold at the end of each day, the graph is 7 distinct points.

The graph is discrete.


How do we use graphs to represent real world relationships

Example 3

Water tank

Water Level

Time

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

Henry begins to drain a water tank by opening a valve. Then he opens another valve. Then he closes the first valve. He leaves the second valve open until the tank is empty.

As time passes while draining the tank (moving left to right along the x-axis) the water level (y-axis) does the following:

• initially declines

• decline more rapidly

• and then the decline slows down.

The graph is continuous.


How do we use graphs to represent real world relationships

Writing Situations for Graphs

Write a possible situation for the given graph.

Step 1 Identify labels. x-axis: time y-axis: speed

Step 2 Analyze sections. over time, the speed:

• initially declines,

• remains constant,

• and then declines to zero.

Possible Situation:

A car approaching traffic slows down, drives at a constant speed, and then slows down until coming to a complete stop.


How do we use graphs to represent real world relationships

Check It Out! Example 2a

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

Jamie is taking an 8-week keyboarding class. At the end of each week, she takes a test to find the number of words she can type per minute. She improves each week.

Each week (x-axis) her typing speed is measured. She gets a separate score (y-axis) for each test.

Since each score is separate, the graph consists of distinct units.

The graph is discrete.


How do we use graphs to represent real world relationships

Lesson Quiz: Part I

1. Write a possible situation for the given graph.

Possible Situation: The level of water in a bucket stays constant. A steady rain raises the level. The rain slows down. Someone dumps the bucket.


How do we use graphs to represent real world relationships

Lesson Quiz: Part II

2. A pet store is selling puppies for $50 each. It has 8 puppies to sell. Sketch a graph for this situation.


  • Login