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

a. ${\displaystyle f(x)=x+2}$ = Function
b. ${\displaystyle g(x)=x-2}$ = Function
c. ${\displaystyle h(x)=x*2}$ = Function
d. ${\displaystyle i(x)=x/2}$ = Function

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

a. ${\displaystyle j(x)=x+x}$ = Function Same as x * 2.
b. ${\displaystyle k(x)=x-x}$ = Function
c. ${\displaystyle l(x)=x*x}$ = Function
d. ${\displaystyle m(x)=x/x}$ = Function

3. Can you write descriptions of the functions in problems 1 and 2? What is the difference?

The functions in exercise 1 use the variable and a constant. The functions in exercise 2 depend on the value of the variable x. All of these examples are functions because each input is mapped to at most one output, although notice that in the case of ${\displaystyle m(x)}$ it is not defined for ${\displaystyle x=0}$. ${\displaystyle x+x}$ shows the relationship between addition and multiplication. ${\displaystyle x*x}$ shows a similar relationship between multiplication and exponentiation. ${\displaystyle x-x}$ and ${\displaystyle x/x}$ show the identity property of subtraction and division respectively. (What are the identity properties of addition and multiplication? Are these functions or relationships?)