Question

Definition of a Function Which of the following statements describe a functions?

(a) A persons income is a function of their place of residence
(b)A towns yearly average crime rate is a function of the year.
(c) A amount of revenue a bicycle company makes is a function of how many bicycles are sold.
(d) The number of meters walked is a function of the average rate of travel x

Answer 1

A function is a mathematical relationship between an input and an output. Statements (b) and (c) describe functions, while statements (a) and (d) do not.

Step-by-step explanation:

A function is a mathematical relationship between two sets of values, called the input (independent variable) and the output (dependent variable). In a function, each input has exactly one corresponding output. To determine whether a statement represents a function, we need to check if each input yields a unique output.

1. (a) A person's income is a function of their place of residence. This is not a function because two people living in the same place can have different incomes.
2. (b) A town's yearly average crime rate is a function of the year. This is a function because for each year, there is a unique average crime rate.
3. (c) The amount of revenue a bicycle company makes is a function of how many bicycles are sold. This is a function because the number of bicycles sold determines the revenue.
4. (d) The number of meters walked is a function of the average rate of travel. This is not a function because different average rates of travel can result in the same number of meters walked.