Graphing Relationships

Vocabulary Copy the following 2 slides in your INB Continuous graph Discrete graphs

Continuous A graph made up of connected lines 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

Start the Video

Continuous and Discrete Length of hair over a month Number of cars in the parking lot over a 24 hour period Student enrollment at Kleb 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

Graphs can be used to illustrate many different situations 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.

Example 1: 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.

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… Each day several leaves fall Wind blows off many leaves Eventually no more leaves 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.

Check It Out! 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 .

Check It Out! 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.

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

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

Example 2B: Sketching Graphs for Situations 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.

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.

The graph is continuous. Check It Out! Example 2b 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.

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.

Example 3: 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.

Check It Out! Example 3 Write a possible situation for the given graph Step 1 Identify labels. x-axis: students y-axis: pizzas Step 2 Analyze sections. As students increase, the pizzas do the following: • initially remains constant, • and then increases to a new constant. Possible Situation: When the number of students reaches a certain point, the number of pizzas bought increases.

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.

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

Sketch a graph for the given situation Sketch a graph for the given situation. Tell whether the graph is discrete or continuous. 1. A giraffe is born 6 feet tall and continues to grow at a steady rate until it is full grown. height time

Sketch a graph for the given situation Sketch a graph for the given situation. Tell whether the graph is discrete or continuous. 1. A giraffe is born 6 feet tall and continues to grow at a steady rate until it is full grown. height time continuous

2. The price of a used car is discounted $200 each week. Sketch a graph for the given situation. Tell whether the graph is discrete or continuous. 2. The price of a used car is discounted $200 each week. Price Weeks

Sketch a graph for the given situation Sketch a graph for the given situation. Tell whether the graph is discrete or continuous. 2. The price of a used car is discounted $200 each week. Price Weeks discrete

Sketch a graph for the given situation Sketch a graph for the given situation. Tell whether the graph is discrete or continuous. 3. A city planner buys more buses as the population of her city grows.. Number of Buses Population

Sketch a graph for the given situation Sketch a graph for the given situation. Tell whether the graph is discrete or continuous. 3. A city planner buys more buses as the population of her city grows.. Number of Buses Population discrete

Sketch a graph for the given situation Sketch a graph for the given situation. Tell whether the graph is discrete or continuous. 4. 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

Sketch a graph for the given situation Sketch a graph for the given situation. Tell whether the graph is discrete or continuous. 4. 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

Sketch a graph for the given situation Sketch a graph for the given situation. Tell whether the graph is discrete or continuous. 5. Mrs. Hubbard has the flu and her temperature rises slowly until it reaches 101º. Temperature time

Sketch a graph for the given situation. 5. Mrs. Hubbard has the flu and her temperature rises slowly until it reaches 101º. Temperature time

6. Leon puts ice cubes in his soup to cool it down before eating it. Sketch a graph for the given situation. Tell whether the graph is discrete or continuous. 6. Leon puts ice cubes in his soup to cool it down before eating it. Temperature time

6. Leon puts ice cubes in his soup to cool it down before eating it. Sketch a graph for the given situation. 6. Leon puts ice cubes in his soup to cool it down before eating it. Temperature time

Sketch a graph for the given situation Sketch a graph for the given situation. Tell whether the graph is discrete or continuous. 7. Cara turns on the oven and sets it to 300º. She bakes a tray of cookies and then turns the oven off. Temperature time

Sketch a graph for the given situation. 7. Cara turns on the oven and sets it to 300º. She bakes a tray of cookies and then turns the oven off. Temperature time