1. Which of the following definitions are functions and which are relations:
- a. = Function
- b. = Function
- c. = Function
- d. = Function
2. Which of the following definitions are functions and which are relations:
- a. = Function Same as x * 2.
- b. = Relation
- c. = Relation
- d. = Relation
3. Can you write descriptions of the functions in problems 1 and 2? What is the difference?
The functions in exercise 1 use a variable and a constant. The function and relationships in exercise 2 depend on the value of the variable x. In exercise 1 the functions are guaranteed to be unique because x is changed in a consistent way. In question 2 the last three functions are relations because the function value can re-occur. K(x) is a relation because for any value of x the answer will always be 0, l(x) is a relation because it has the the same values for positive and negative values of x, and m(x) has two values: either 1 or -1 and is undefined at 0. When we evaluate the relationships of the variables in terms of themselves we begin to explore the functionality of the operators. shows the relationship between addition and multiplication. shows a similar relationship between multiplication and exponentiation. (Is a function or a relation?) and show the identity property of subtraction and division respectively. (What are the identity properties of addition and multiplication? Are these functions or relationships?)