Graphing Functions with the TI-73

Graphing Calculator Project: Functions
Imagine yourself at the service station, filling your tank with gasoline priced at $1.299 per gallon. If you purchase 10 gallons of gas, your bill will be $12.99, and if you put 13.28 gallons in your tank, your bill (rounded to the penny) will be $17.25. The general principle is that your bill that day at the station is a function of the amount of gasoline you purchase. If we let the letter x represent the number of gallons of gasoline purchased and let the letter y represent the final bill, then y is given by the simple rule y = $1.299x. Nicely enough, the pump carries out this calculation right before our eyes and, as the values of x whirl by on one display of the pump, we can simultaneously watch the corresponding values of y on another display. A graphing calculator can give us a graphical representation of the number of gallons versus the total cost. Instructions on how to use the TI-73 can be found in your textbook in Appendix C. Start by graphing the rule y = $1.299x then go to the table and compare the x and y values. What would be an appropriate window setting for this function?

Tortoise and hare picture
Graphing the Achilles versus the Tortoise Race
 Achilles and the Tortoise have agreed to compete in a 1000-yard race. At the starting signal, the tortoise lumbers off at a steady 3.8 feet per second (which is actually extremely fast for a tortoise!). Achilles, who knows he runs much faster than the tortoise, grandstands in front of the crowd, and finally, after horsing around for 10 minutes, takes off for the finish line at a steady 14.7 feet per second. Does Achilles win the race, or has he been overconfident? Write a function for the Tortoise and for Achilles, then use the TI-73 to graph both functions and the 1000-yard finish line (Y3 = 1000 yards = ? feet) in an appropriate window. Use the trace feature on the TI-73 to find out who crosses the 1000-yard line first. You can use the zoom feature to zoom in on the finish line.

Updated: 08/21/2003
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