Question

marking period 2 common assessment feb 3 - 11:00 am a hardware store rents vacuum cleaners that customers may use for part or all of a day, up to 12 hours, before returning. the store charges a flat fee plus an hourly rate. write a linear function f for the total rental cost of a vacuum cleaner. hours cost ($) 1 20 1.5 23 2 26 2.5 29 3 32 a. ( f(x) = 6x + 14 ) b. ( f(x) = 3x + 14 ) c. ( f(x) = 3x + 22 ) d. ( f(x) = 6x + 24 ) part b flat fee the store charges = $ a reasonable domain for the function is: ( < x leq ) cost to rent a vacuum for 7 hours = $

Explanation:

Part B: Flat fee the store charges

Step1: Recall linear function form

A linear function is \( f(x) = mx + b \), where \( m \) is the hourly rate (slope) and \( b \) is the flat fee (y - intercept). From the selected option (A: \( f(x)=6x + 14 \)) or by calculating slope and intercept:

• Using two points, e.g., \( (1, 20) \) and \( (2, 26) \). Slope \( m=\frac{26 - 20}{2 - 1}=6 \).
• Substitute \( x = 1 \), \( y = 20 \) into \( f(x)=mx + b \): \( 20=6(1)+b \Rightarrow b = 14 \). So flat fee \( b = 14 \).

A reasonable domain for the function:

Step1: Determine time constraints

The store allows up to 12 hours, and time can’t be negative (or less than 0, as you can’t rent for negative hours). So domain is \( 0 < x\leq12 \) (assuming \( x \) is hours, \( x > 0 \) since you rent for part or all of a day, not zero hours).

Cost to rent a vacuum for 7 hours:

Step1: Use the linear function

From option A, \( f(x)=6x + 14 \). Substitute \( x = 7 \):
\( f(7)=6(7)+14 \)

Step2: Calculate

\( 6(7)=42 \), \( 42 + 14 = 56 \).

Part B Answer:

Answer:

14

Domain Answer: