Answer:
[tex]Domain: \{0,1,2,3,4,5,6\}[/tex]
Step-by-step explanation:
Given
[tex]m = 45 - 7.5b[/tex]
[tex]Values: \{0,1,2,3,4,5,6,7,8,9,10\}[/tex]
Required
Select all values that belongs to the domain of the given function
Analyzing the question;
The question says that the function, m represent the amount left after buying b number of books
This means that, after purchasing b books, I'm expected to have a certain m amount of dollars left with me;
This implies that the value of m can never be negative;
So, the domain of m are values of b such that [tex]m \geq 0[/tex]
When b = 0
[tex]m = 45 - 7.5(0)[/tex]
[tex]m = 45 - 0[/tex]
[tex]m = 45[/tex]
When b = 1
[tex]m = 45 - 7.5(1)[/tex]
[tex]m = 45 - 7.5[/tex]
[tex]m = 37.5[/tex]
When b = 2
[tex]m = 45 - 7.5(2)[/tex]
[tex]m = 45 - 15[/tex]
[tex]m = 30[/tex]
When b = 3
[tex]m = 45 - 7.5(3)[/tex]
[tex]m = 45 - 22.5[/tex]
[tex]m = 22.5[/tex]
When b = 4
[tex]m = 45 - 7.5(4)[/tex]
[tex]m = 45 - 30[/tex]
[tex]m = 15[/tex]
When b = 5
[tex]m = 45 - 7.5(5)[/tex]
[tex]m = 45 - 37.5[/tex]
[tex]m = 7.5[/tex]
When b = 6
[tex]m = 45 - 7.5(6)[/tex]
[tex]m = 45 - 45[/tex]
[tex]m = 0[/tex]
When b = 7
[tex]m = 45 - 7.5(7)[/tex]
[tex]m = 45 - 52.5[/tex]
[tex]m = -7.5[/tex]
There's no need to check for other values, as they will result in negative values of m;
Hence, the domain of m are:
[tex]Domain: \{0,1,2,3,4,5,6\}[/tex]
The values that are in the domain of the function are 7, 8, 9 and 10
Given the linear function m=45−7.5b
where:
For th domain to exist, then;
45 - 7.5b< 0
7.5 b > 45
b > 45/7.5
b > 6
Hence the values that are in the domain of the function are 7, 8, 9 and 10
Learn more on domain here; https://brainly.com/question/10197594
