Equivalent expressions of functions Equivalent recipes This task presents computing recipes, where you strat out with an arbitrary number and follow the recipe to obtain a new number. Choose any number and operate on it according to the three recipes. Try another number. Explain what is meant by the fact that the three recipes are equivalent. Construct correspondence rules to describe the three recipes. How can you prove that the three correspondence rules are equivalent? Invent another recipe that is equivalent to the three recipes. Invent a recipe that is not equivalent to the three given recipes. Invent other recipes that are equivalent to the recipe you invented. Recipe 1 a Choose any number: b Add 1 to the number in line a and multiply the result by 2: c Add 1 to the number in line b and multiply the result by 2: d Add 1 to the number in line c and multiply the result by 2: Recipe 2 a Choose any number: b Multiply the number in line a by 2: c Add 3 to the number in line b: d Multiply the number in line c by 4: e Add 2 to the number in line d: Recipe 3 a Choose any number: b Add 2 to the number in line a: c Multiply the number in line b by 8: d Subtract 2 from the number in line c:

The form f(x)=ax+b The form f(x)=a(x-c) The form f(x)=a(x-c)+m Emphasizing information Emphasizing intersections Families of functions Features from value tables Partial pictures Equivalent recipes Telephone rates Verbal descriptions of equivalent expressions Stories Describing a trip Speeding car Exercise 1 Exercise 2 Exercise 3 Exercise 4 Exercise 5 Exercise 6 Exercise 7 Exercise 8 Exercise 9 Exercise 10 Exercise 11 Exercise 12 Exercise 13 Exercise 14 Exercise 15 Exercise 16 Exercise 17 Exercise 18 Exercise 19