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: 0 ≤ b ≤ 10

R: 12 ≤ W(b) ≤ 120

B. D: 0 ≤ b ≤ 10

R: 0 ≤ W(b) ≤ 120

C. D: 10 ≤ b ≤ 12

R: 0 ≤ W(b) ≤ 120

D. D: 0 ≤ b ≤ 120

R: 0 ≤ W(b) ≤ 10

Answer 1

Not the best problem. W(b) gives wood as a function of the number of birdhouses. The domain is the set of valid inputs. They're looking for an answer I don't quite agree with but we'll write anyway as

`0 \le b \le 10`

The range is the set of valid outputs. Given this domain, that's

`0 \le W(b) \le 120`

Putting those together gives

Choice B

Answer 2

Correct option is:

B. D: 0 ≤ b ≤ 10

R: 0 ≤ W(b) ≤ 120

Explanation:

Owen has enough materials to build up to 10 birdhouses in shop class.

The function W(b) = 12b represents the total amount of wood that Owen would need to build b birdhouses.

B represents the number of birdhouses which can be up to 10

i.e. 0 ≤ b ≤ 10 (which is the domain)

Multiplying each side of the above inequality by 12

⇒ 0≤ 12b ≤120

⇒ 0 ≤ W(b) ≤ 120 (which is the range)

Hence, Correct option is:

B. D: 0 ≤ b ≤ 10

R: 0 ≤ W(b) ≤ 120