Representations of linear functions Inverse Machines The life span of a dog is around 15 years, so a 12 year old dog is considered old. In the first computing machine below, you can enter a dog's age in standard years and obtain its age in "dog-years." The second computing machine is an inverse machine to the first one. What does this mean? Present the functions represented by the first two computing machines in other representations: correspondence rules, value tables, and graphs. What is the relation between the value tables corresponding to the two machines? The third machine converts distances measured in miles to kilometers. What will the inverse machine do? Construct such a machine using the Computing machine tool. The fourth machine translates the temperature measurement on the Celsius scale to the Fahrenheit scale. What will the inverse machine do? Construct such a machine using the Computing machine tool. 1. Computing machine for translating standard years to dog-years x (age in standard years) f f(x) (age in dog-years) 2. Computing-machine for translating dog-years to standard-years x (age in dog-years) g g(x) (age in standard years) 3. Computing machine for translating miles to kilometers x (miles) h h(x) (kilometers) 4. Computing machine for translating Celsius to Fahrenheit x (temperature in Celsius) k k(x) (temperature in Fahrenheit)

At the gas station Different prices Cab fares Changing grades Fuel efficiency Postal rates Inverse machines Graphs describing motion Trucks Medical prescriptions Height and bone lengths Dividing a budget Electric bill Constructing functions Exercise 1 Exercise 2 Exercise 3 Exercise 4 Exercise 5