Question

practice & problem solving apply 22 apply math models 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 not have on certain weeks and that durations of his classes will vary only as shown in the table for any given week. a. describe the domain and range relating the number of classes to the total weekly class time. b. is the relation a function? explain.

Explanation:

Step1: Define domain and range concepts

The domain is the set of input values (number of classes), and the range is the set of output values (total weekly class - time).

Step2: Calculate total weekly class - time for each week

For Week 1: $60 + 90+45 + 45+0=240$ minutes. For Week 2: $60 + 60+45 + 45+60=270$ minutes. The number of classes is 5 (English, Math, History, Biology, Biology Lab).

Step3: Determine the domain and range

The domain is the set of the number of classes, which is $\{5\}$ (since the number of classes is always 5 in this context). The range is the set of total weekly class - times, which is $\{240,270\}$.

Step4: Check if the relation is a function

A relation is a function if each element in the domain is paired with exactly one element in the range. Here, the domain element 5 is paired with two range elements (240 and 270).

Answer:

a. Domain: $\{5\}$, Range: $\{240,270\}$
b. No, because the element 5 in the domain is paired with two different elements (240 and 270) in the range.