For a given function y = f(x), the domain is the set of the possible values of x that we can use in the function, and the range is the set of the possible values of y that the function can return.
We will find that the range is: {3, 9, 15, 21, 27, 33, 39, 45, 51, 57, 63}
And the domain is: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Here the function is:
f(x) = 6*x + 3
Where x is the number of boxes sold.
We know that only 10 students bought popcorn, so what is reasonable domain and range?
Knowing that 10 students bought popcorn, we know that the maximum value that x can take is 10.
Then the domain will be:
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
These are the possible values of x that makes sense to use in our function.
We only use whole numbers as you can not buy a rational number of boxes.
To get the range we just need to evaluate the function in these values (the ones from the domain):
f(0) = 6*0 + 3 = 3
f(1) = 6*1 + 3 = 9
f(2) = 6*2 + 3 = 15
f(3) = 6*3 + 3 = 21
f(4) = 6*4 + 3 = 27
f(5) = 6*5 + 3 = 33
f(6) = 6*6 + 3 = 39
f(7) = 6*7 + 3 = 45
f(8) = 6*8 + 3 = 51
f(9) = 6*9 + 3 = 57
f(10) = 6*10 + 3 = 63
Then the range is just:
{3, 9, 15, 21, 27, 33, 39, 45, 51, 57, 63}
If you want to learn more, you can read:
https://brainly.com/question/1632425
