Question

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?
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:
\[
0 \leq b \leq 10
\]

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:
\[
0 \leq W(b) \leq 120
\]

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

C.
D: 0 ≤ b ≤ 10
R: 0 ≤ W(b) ≤ 120