From Graphs of Lines to Functions of Lines
Intro
Now that we've explored lines and their functions, let us try to create functions that describe the graphs of lines. Functions can create graphs, but they can also describe graphs that already exist. Later on in this course, we will create graphs and then create functions that describe the graphs.
Problem 1: Dr. Jones Finds the Hidden Temple
Dr. Jones is a world renowned archaeologist. He is searching for a hidden temple on a mysterious island off the east coast of Africa. Dr. Jones is seven miles above the equator on a portion of African coastline that is flat. The island which he believes to contain the temple is four miles east and three miles north. Dr. Jones wishes to travel to the island in the shortest route possible and, as the mathematical addage goes, "the shortest route between two points is a straight line".
With a partner, represent the path that Dr. Jones must take using a graph.
Activity: Class Discussion
What is the equation of the line for the graph?
Problem 2: Fig Newton and the Counter-intuitive Liquid
Fig Newton is Isaac Newton's cousin. He has had to stand in his cousin's shadow, but at least he has a cookie named after him. What is more, Fig has made a scientific discovery of his own. Fig has unearthed a strange liguid which becomes colder as it is heated. Fig notes that before he starts heating the liquid, it is at a temperature of 30 degrees Celsius. As Fig heats the liquid, it's temperature drops by one degree every two minutes it is heated.
With a partner, represent the temperature of the liquid as time passes using a graph.
Activity: Class Discussion
What is the equation of the line for the graph?
Reflection
How can functions be used to describe graphs? What have you learned?