# 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 ≤ 120 r: 0 ≤ w(b) ≤ 10 d: d: 0 ≤ b ≤ 10 r: 0 ≤ w(b) ≤ 120

120

Step-by-step explanation:

A: D: 10 ≤ b ≤ 12

R: 0 ≤ W(b) ≤ 120

B: D: 0 ≤ b ≤ 10

R: 12 ≤ W(b) ≤ 120

C: D: 0 ≤ b ≤ 120

R: 0 ≤ W(b) ≤ 10

D: D: 0 ≤ b ≤ 10

R: 0 ≤ W(b) ≤ 120

W(b) = 12b.

he has enough to build 10 birdhouses, he doesn't have for more than that, he can either build no birdhouses or build 10 birdhouses, since "b" is the independent variable and thus the domain will come from it, what values can "b" safely take? "b" can be either 0 or more than 0 but nor more than 10, because Owen doesn't have enough for more than that, 0 ≤ b ≤ 10.

let's say owen chooses to build 0 birdhouses, then W(0) = 12(0) => W(0) = 0.

let's say owen chooses to build 10 birdhouses, then W(10) = 12(10) => W(10) = 120.

so the amount of wood needed for those birdhouses, namely the range, can be either 0, if he chooses to build none, or 120 if he chooses to build 10, 0 ≤ W(b) ≤ 120.

A. D: 0 ≤ b ≤ 10 R: 0 ≤ W(b) ≤ 120

Step-by-step explanation:

Since b represents the number of birdhouses, it is reasonable for that to have non-negative values. The maximum material availability means that b > 10 is not of practical use. This eliminates choices B and D.

Since W represents the amount of wood required for b birdhouses, it is reasonable for the range of it to match 12 times the domain: 12·0 = 0 to 12·10 = 120. This eliminates choice C.

The appropriate choice is ...

A. D: 0 ≤ b ≤ 10 R: 0 ≤ W(b) ≤ 120

D. D: 0 ≤ b ≤ 10; R: 0 ≤ W(b) ≤ 120

Step-by-step explanation:

The problem statement tells you Owen can build up to 10 birdhouses, and that b represents that number. Then 0 ≤ b ≤ 10 is the domain described by the problem statement.

It also tells you that W(b) = 12b, so filling in values from 0 to 10 gives a range from 0 to 120: 0 ≤ W(b) ≤ 120.

These observations match choice D.

B. D: 0 ≤ b ≤ 10 R: 0 ≤ W(b) ≤ 120

Step-by-step explanation:Each birdhouse uses 12 sq ft of wood.

He has enough to build 10 birdhouses, so he has 120 sq ft of wood.

The function has an input of the number of birdhouses, b, and has an output of the amount of wood needed, W. b is the input or the domain, and W is the output or the range. The domain is 0 to 10. The range is 0 to 120.

Correct option is:

B. D: 0 ≤ b ≤ 10

R: 0 ≤ W(b) ≤ 120

Step-by-step 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

Each birdhouse uses 12 sq ft of wood.

He has enough to build 10 birdhouses, so he has 120 sq ft of wood.

The function has an input of the number of birdhouses, b, and has an output of the amount of wood needed, W. b is the input or the domain, and W is the output or the range. The domain is 0 to 10. The range is 0 to 120.

C

Each birdhouse uses 12 sq ft of wood.

He has enough to build 10 birdhouses, so he has 120 sq ft of wood.

The function has an input of the number of birdhouses, b, and has an output of the amount of wood needed, W. b is the input or the domain, and W is the output or the range. The domain is 0 to 10. The range is 0 to 120.

B. D: 0 ≤ b ≤ 10 R: 0 ≤ W(b) ≤ 120

Enjoy! Hope this helped you! :)

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

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

Putting those together gives

Choice B