Owen has enough materials to build up to 10 birdhouses in shop class. Each birdhouse needs 12 square feet of wood. The function W(b) = 12b represents the total amount of wood that Owen would need to build b birdhouses. What domain and range are reasonable for the function?

Question

A.
D: 10 ≤ b ≤ 12
R: 0 ≤ W(b) ≤ 120
B.
D: 0 ≤ b ≤ 10
R: 12 ≤ W(b) ≤ 120
C.
D: 0 ≤ b ≤ 10
R: 0 ≤ W(b) ≤ 120
D.
D: 0 ≤ b ≤ 120
R: 0 ≤ W(b) ≤ 10

Answer 1

To determine the reasonable domain and range for the function W(b) = 12b, where b is the number of birdhouses Owen can build:

1. Domain:

   • Since Owen can build from 0 up to a maximum of 10 birdhouses, the domain of b will be: $$0\le b\le 10$$

2. Range:

   • If b represents the number of birdhouses, then the total amount of wood W(b) needed can be calculated from the function: $$W(b)=12b$$
   • When b = 0 (he builds no birdhouses), W(0) = 12 * 0 = 0.
   • When b = 10 (he builds the maximum of 10 birdhouses), W(10) = 12 * 10 = 120.
   • Thus, the range of W(b) will be: $$0\le W(b)\le 120$$

Putting together the domain and range, the appropriate choice is:

C. D: 0 ≤ b ≤ 10
R: 0 ≤ W(b) ≤ 120