Activator – 9/12/08 • Turn to P. 43 and read the passage at the top of the page. Answer the following questions. • What does point B on the graph represent? • About what percent of normal blood flow occurs two days after the injury? • Does the blood flow to the brain increase evenly from the day of the injury to day 6? Explain your answer. • What feature of the graph shows the rate of increase in blood flow?
How are graphs of functions interpreted and how are graphs of functions drawn? • A function is a relationship between input and output. • In a function, the output depends on the input. • There is exactly one output for each input. • See diagram of the Coordinate Plane P. 43.
A function is composed of an independent variable and a dependent variable. • Independent variable - the variable in a function whose value is subject to choice. • Dependent variable – the variable in a relationship whose value depends on the value of the independent variable. • Think back to the activator. Name the independent variable and the dependent variable. • See P. 44 Example 2 • Your Turn . . . . . .
Example - • In warm climates, the average amount of electricity used in homes each month rises as the daily average temperature increases, and falls as the daily average temperature decreases. Identify the independent and dependent variables in the function of temperature and electricity used. • (overhead example) • Example 3 – Functions can be graphed without a scale on either axis to show the general shape of the graph that represents a function.
Graphs can be used to represent many real-world situations. • There are three lunch periods at Rugby Middle School Cafeteria. During the first period, 352 students eat lunch. During the second period, 304 students eat lunch, during third period 391 students eat lunch. • A. Make a table showing the number of students for each period. • B. Write the data as a set of ordered pairs. • C. Draw a graph that shows the relationship between the lunch period and the number of students. • What the features of a good graph?
Domain and Range • A set of ordered pairs is called a relation. • The set of the first numbers of the ordered pairs is the domain. The domain contains all values of the independent variable. • The set of second numbers of the ordered pairs is the range of the relation. The range contains all values of the dependent variable. (x,y) x = domain values y = range values
Let’s do it again! The Buccaneer Team is planning a trip to the creek this month. The cost is $3.00 per person, and at most, 105 students will go. • Identify a reasonable domain and range for this situation. • Draw a graph that shows the relationship between the number of students who go to the creek, and the total price of the trip.
Drawing graphs to demonstrate relationships • Draw a graph that represents the height of a skydiver just before she jumps from a plane until she lands. • Draw a graph that represents the following description of Fred’s checking account: Fred has a beginning balance around $150. He buys about $50 of gas and writes a check. Friday is payday! He deposits his paycheck of $550. He goes by the ATM and withdraws $30 for RMS night at Fun Depot.
More Fun! • The roller coaster goes down a small hill, coasts at about the same speed, increases in speed on the way down the hill, decreases again on the way up the hill, increases down another hill, and then slows down for the end of the ride. • The jogger increases in speed as he begins and then runs about the same speed for a while. He increases again and runs at this faster speed for a while. Then he decreases, maintains a speed, and finally slows down at the finish of the run.
Summarizer • 3 things your learned about graphs of funtions. • 2 ways to remember what you learned. • 1 thing you still have a question about.