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: 0 ≤ b ≤ 10
R: 12 ≤ W(b) ≤ 120
B.
D: 0 ≤ b ≤ 120
R: 0 ≤ W(b) ≤ 10
C.
D: 10 ≤ b ≤ 12
R: 0 ≤ W(b) ≤ 120
D.
D: 0 ≤ b ≤ 10
R: 0 ≤ W(b) ≤ 120
The correct answer is D.
The domain (input values) of the function should be within the range of reasonable values for the number of birdhouses Owen can build. Since Owen has enough materials to build up to 10 birdhouses, the domain should be 0 ≤ b ≤ 10.
The range (output values) of the function should be within the range of reasonable values for the total amount of wood needed to build the birdhouses. Each birdhouse needs 12 square feet of wood, so the minimum amount of wood needed is 0 (for building 0 birdhouses) and the maximum amount of wood needed is 12 multiplied by the number of birdhouses (10) which is 120. Therefore, the range should be 0 ≤ W(b) ≤ 120.