Question

synthesis
a toy factory uses this diagram and function to determine the width of the bow tie. all units are in inches.
what does ( b(x) = 2x + 1 ) mean in this situation?
what does ( b(4) = 9 ) mean?
( b(x) = 2x + 1 ) means...
( b(4) = 9 ) means...

Explanation:

For \( b(x) = 2x + 1 \): In the context of the toy factory, \( x \) likely represents some related measurement (e.g., the width of a central part of the bow - tie or another component), and \( b(x) \) represents the width of the bow - tie. The function means that to find the width of the bow - tie (\( b(x) \)), we take twice the value of \( x \) (the related measurement) and add 1 inch.

For \( b(4)=9 \): When \( x = 4 \) (the related measurement is 4 inches), substituting \( x = 4 \) into the function \( b(x)=2x + 1 \), we get \( b(4)=2\times4 + 1=9 \). This means that when the related measurement \( x \) is 4 inches, the width of the bow - tie \( b(x) \) is 9 inches.

Answer:

• \( b(x)=2x + 1 \) means: The width of the bow - tie (\( b(x) \)) in inches is equal to twice a related measurement \( x \) (in inches) plus 1 inch.
• \( b(4) = 9 \) means: When the related measurement \( x \) is 4 inches, the width of the bow - tie is 9 inches.