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
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
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
To relate a graph to a given situation, use key words in the description.
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.
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 upwardGraph C Horizontal Graphs A, B, and C 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. Example 1 Continued
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.
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. The graph is continuous. Speed Time y x 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
When sketching or interpreting a graph, pay close attention to the labels on each axis. Helpful Hint
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 graph is discrete. 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.
Sketch a graph for the situation. Tell whether the graph is continuous or discrete. Example 4 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. Water tank Water Level Time 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.
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.
Example 5 Write a possible situation for the given graph. A car approaching traffic slows down, drives at a constant speed, and then slows down until coming to a complete stop. 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:
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. Example 6
Example 7 A giraffe is born 6 feet tall and continues to grow at a steady rate until it is full grown. height time
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
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
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
Ms. Langlinais has the flu and her temperature rises slowly until it reaches 101º. Temperature time Example 9
5. Ms. Langlinais has the flu and her temperature rises slowly until it reaches 101º. Temperature time Example 9 (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 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 Example 10 (cont)