1. DCA Answers 1. D 2. F 3. A 4. H 5. A 6. G 7. B 8. H 9. D 10. F 11. B
14. J
15. D
16. J
17. D
18. G
19. A
20. F

2. Graphing Relationships

3. Vocabulary
Continuous graph
Discrete graphs

4. Continuous A graph made up of connected lines, line segments or curves
Data that changes over time
Measurements changing over time
Measured data
Height, weight, temperature shown over a period of time

5. Discrete A graph made up of unconnected points
Data that is counted or data that is measured in distinct time segments (each day, each year, each hour, etc)
People, chairs, cars, leaves on tree, umbrellas, etc
Counted data

6. Continuous or Discrete
Length of hair over a month
Number of cars in the parking lot over a 24 hour period
Student enrollment at Strack over 2 years
Rainfall totals each month for the summer
Number of desks in a classroom over the year
Time you walk your dog each day for a week

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

8. 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 .

9. Step 2 List key words in order and decide which graph shows them.
Example 1 Continued
Step 2 List key words in order and decide which graph shows them.
Key Words
Segment Description
Graphs…
Increased
steadily
Remained constant
Increased slightly before dropping sharply
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.

10. 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.

11. The graph is continuous.
Example 2
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:
Speed
Time y x
• initially increases
• remains constant
• decreases to a stop
• increases
The graph is continuous.

12. When sketching or interpreting a graph, pay close attention to the labels on each axis.
Helpful Hint

13. Example 3
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.

14. The graph is continuous.
Example 4
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:
Water tank
Water Level
Time
• initially declines
• decline more rapidly
• and then the decline slows down.
The graph is continuous.

15. Both graphs show a relationship about a child going down a slide
Both graphs show a relationship about a child going down a slide. Graph A represents the child’s distance from the ground related to time. Graph B represents the child’s Speed related to time.

16. Example 5
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.

17. Example 6
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.

18. Example 7
A giraffe is born 6 feet tall and continues to grow at a steady rate until it is full grown.
height
time

19. Example 7 (cont)
A giraffe is born 6 feet tall and continues to grow at a steady rate until it is full grown.
height
time
continuous

20. Example 8
Ms. Hughes is sky-diving. At first, she is free-falling rapidly and then she releases her parachute to slow her descent until she reaches the ground.
Height Above Ground
time

21. Example 8 (cont)
Ms. Hughes is sky-diving. At first, she is free-falling rapidly and then she releases her parachute to slow her descent until she reaches the ground.
Height Above Ground
time
continuous

22. Example 9
Ms. Langlinais has the flu and her temperature rises slowly until it reaches 101º.
Temperature
time

23. Example 9 (cont)
5. Ms. Langlinais has the flu and her temperature rises slowly until it reaches 101º.
Temperature
time

24. Example 10
Cara turns on the oven and sets it to 300º. She bakes a tray of cookies and then turns the oven off.
Temperature
time

25. Example 10 (cont)
Cara turns on the oven and sets it to 300º. She bakes a tray of cookies and then turns the oven off.
Temperature
time