Problem 116 - College Algebra Essentials

Question

For people filing a single return, federal income tax is a function of adjusted gross income because for each value of adjusted gross income there is a specific tax to be paid. By contrast, the price of a house is not a function of the lot size on which the house sits because houses on same-sized lots can sell for many different prices. a. Describe an everyday situation between variables that is a function. b. Describe an everyday situation between variables that is not a function.

Step-by-Step Solution

Answer

a. An everyday situation that represents a function is assigning unique student roll numbers in a school. b. An everyday example of a situation that is not a function is where the same model of a laptop sold by different vendors can have varying prices.

Step 1: Determine a situation that represents a function

A situation that depicts a function is teaching in a school. In this scenario, each student is assigned a unique roll number. Regardless of the student's name or other attributes, the roll number for a student is always unique. So here, the students' names are the input, and their respective unique roll numbers are the output. This represents a function, since each name is associated with a unique roll number.

Step 2: Determine a situation that does not represent a function

A situation that doesn't represent a function is different brands selling a particular type of product, for instance, a laptop. A single model of laptop can be sold for different prices by different vendors even though the product's characteristics are the same. Thus, in this case, there isn't a unique association from the brand of the laptop to its price. This is an example of a situation that is not a function.