Algebra/Functions/Answers1

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1. Which of the following definitions are functions and which are relations:

a. f(x) = x + 2 = Function
b. g(x) = x - 2 = Function
c. h(x) = x * 2 = Function
d. i(x) = x / 2 = Function

2. Which of the following definitions are functions and which are relations:

a. j(x) = x + x = Function Same as x * 2.
b. k(x) = x - x = Relation
c. l(x) = x * x = Relation
d. m(x) = x / x = 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. x + x shows the relationship between addition and multiplication.  x * x shows a similar relationship between multiplication and exponentiation. (Is n(x) = x * x * x a function or a relation?) x - x and x / x show the identity property of subtraction and division respectively. (What are the identity properties of addition and multiplication? Are these functions or relationships?)