4 Continuous A graph made up of connected lines, line segments or curves Data that changes over timeMeasurements changing over timeMeasured dataHeight, 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, etcCounted data
6 Continuous or Discrete Length of hair over a monthNumber of cars in the parking lot over a 24 hour periodStudent enrollment at Strack over 2 yearsRainfall totals each month for the summerNumber of desks in a classroom over the yearTime 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 1The 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 ContinuedStep 2 List key words in order and decide which graph shows them.Key WordsSegment DescriptionGraphs…IncreasedsteadilyRemained constantIncreased slightly before dropping sharplySlanting upwardGraph CGraphs A, B, and CHorizontalSlanting upward and then steeply downwardGraphs B and CStep 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 graphsThe 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 2Sketch 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:SpeedTimeyx• initially increases• remains constant• decreases to a stop• increasesThe graph is continuous.
12 When sketching or interpreting a graph, pay close attention to the labels on each axis. Helpful Hint
13 Example 3Sketch 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 4Sketch 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 tankWater LevelTime• 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 5Write a possible situation for the given graph.Step 1 Identify labels x-axis: time y-axis: speedStep 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 6Write 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 7A giraffe is born 6 feet tall and continues to grow at a steady rate until it is full grown.heighttime
19 Example 7 (cont)A giraffe is born 6 feet tall and continues to grow at a steady rate until it is full grown.heighttimecontinuous
20 Example 8Ms. 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 Groundtime
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 Groundtimecontinuous
22 Example 9Ms. Langlinais has the flu and her temperature rises slowly until it reaches 101º.Temperaturetime
23 Example 9 (cont)5. Ms. Langlinais has the flu and her temperature rises slowly until it reaches 101º.Temperaturetime
24 Example 10Cara turns on the oven and sets it to 300º. She bakes a tray of cookies and then turns the oven off.Temperaturetime
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.Temperaturetime