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

Explanation:

Step1: Analyze the domain (b)

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

Step2: Analyze 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 the range \( R \) is \( 0 \leq W(b) \leq 120 \).

Answer:

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