Question

select the correct answer
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 leq b leq 10 )
( r: 0 leq w(b) leq 120 )

b. ( d: 0 leq b leq 120 )
( r: 0 leq w(b) leq 10 )

c. ( d: 0 leq b leq 10 )
( r: 12 leq w(b) leq 120 )

d. ( d: 10 leq b leq 12 )
( r: 0 leq w(b) leq 120 )

Explanation:

Step1: Analyze the domain (b values)

Owen can build 0 to 10 birdhouses (since he has materials for up to 10). So domain \( D: 0 \leq b \leq 10 \).

Step2: Analyze the range (W(b) values)

Use \( W(b)=12b \). When \( b = 0 \), \( W(0)=12(0)=0 \). When \( b = 10 \), \( W(10)=12(10)=120 \). So range \( R: 0 \leq W(b) \leq 120 \).

Step3: Match with options

Option A has \( D: 0 \leq b \leq 10 \) and \( R: 0 \leq W(b) \leq 120 \), which matches our analysis.

Answer:

A. D: \( 0 \leq b \leq 10 \), R: \( 0 \leq W(b) \leq 120 \)