Question

the table shows the number of minutes drew spends in each class for each of two weeks. assume that biology lab is the one class drew may or may not have on certain weeks, and that the duration of each class will only be one of the times shown in the table for any given week. complete parts (a) and (b)

a. describe the domain and range relating the number of classes to the total weekly class time
what is the domain? select the correct choice below, and fill in the answer box to complete your choice.
a. the domain is {x | x = } (type your answer(s) as whole numbers. use a comma to separate answers as needed.)
b. the domain is {x | } (type an inequality or a compound inequality)

class | week 1 time (min) | week 2 time (min)
english | 60 | 60
math | 90 | 60
history | 45 | 45
biology | 45 | 45
biology lab | 0 | 60

Explanation:

Step1: Understand the domain concept

The domain is the set of all possible input values (in this case, the number of classes).

Step2: Analyze the classes

Looking at the table, the classes are Biology Lab, Biology, History, Math, English. So the number of classes \(x\) can be \(1,2,3,4,5\) (whole numbers).

Answer:

B. The domain is \(\{x|x = 1,2,3,4,5\}\) (assuming each class is a distinct input for the relation of class - time. If we consider the classes as individual entities for the domain of the relation mapping classes to time, and since there are 5 classes, the domain elements (number of classes considered as input) are the whole numbers representing the count of classes we can pick from the set of 5 classes. So the domain is the set of whole numbers \(1,2,3,4,5\) as we can have 1 class (e.g., only Biology Lab), 2 classes (e.g., Biology Lab and Biology) and so on up to 5 classes. So in set - builder notation for whole numbers \(x\), it is \(\{x|x = 1,2,3,4,5\}\))