What are your objectives for Section 4.5? How can you accomplish each objective? 6 Define and Graph a Linear Function • Learn the defi nition of a linear function. Write your own example in your notes. • Be able to graph a linear function using the slope and y-intercept. • Complete the given example on your own. • Complete You Try 9. 7 Solve Problems Using Linear Functions • Know how to label the graph for a linear function. • Be able to choose a meaningful variable for the independent variable and the function. • Understand the meaning of function values. • Complete the given example on your own. Read the explanations, follow the examples, take notes, and complete the You Trys. If you are driving on a highway at a constant speed of 60 miles per hour, the distance you travel depends on the amount of time spent driving. Driving Time Distance Traveled 1 hr 60 mi 2 hr 120 mi 2.5 hr 150 mi 3 hr 180 mi We can express these relationships with the ordered pairs (1, 60) (2, 120) (2.5, 150) (3, 180) where the fi rst coordinate represents the driving time (in hours), and the second coordinate represents the distance traveled (in miles). We can also describe this relationship with the equation y 60x where y is the distance traveled, in miles, and x is the number of hours spent driving. The distance traveled depends on the amount of time spent driving. Therefore, the distance traveled is the dependent variable, and the driving time is the independent variable. In terms of x and y, since the value of y depends on the value of x, y is the dependent variable and x is the independent variable. 1 Define and Identify Relations, Functions, Domain, and Range If we form a set of ordered pairs from the ones listed above, we get the relation {(1, 60), (2, 120), (2.5, 150), (3, 180)}. Definition A relation is any set of ordered pairs. www.mhhe.com/messersmith SECTION 4.5 Introduction to Functions 197
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