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

Explanation:

Step1: Determine the domain (b)

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

Step2: Determine the range (W(b))

The function is \( W(b) = 12b \). When \( b = 0 \), \( W(0) = 0 \). When \( b = 10 \), \( W(10) = 12\times10 = 120 \). So \( 0 \leq W(b) \leq 120 \).

Step3: Match with options

Check each option:

• A: Domain \( 10 \leq b \leq 12 \) is wrong (b can be 0 - 10).
• B: Domain \( 0 \leq b \leq 10 \), Range \( 0 \leq W(b) \leq 120 \) matches.
• C: Range \( 0 \leq W(b) \leq 10 \) is wrong (W(b) = 12b, max at b=10 is 120).
• D: Domain \( 0 \leq b \leq 10 \), but Range \( 12 \leq W(b) \leq 120 \) is wrong (W(0)=0).

Answer:

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