Question

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.
A. f(x) = 6x + 14
B. f(x) = 3x + 14
C. f(x) = 3x + 22
D. f(x) = 6x + 24

Flat fee the store charges =

A reasonable domain for the function is: =

Cost to rent a vacuum for 7 hours =

Answer 1

The flat fee that the store charges is $14 and the cost for 7 hours is $56

A linear equation is on the form:

y = mx + b

where y, x are variables, m is the rate of change and b is the initial value of y.

let f for the total rental cost of a vacuum cleaner for x hours

Using the points (1, 20) and (3, 32) from the table:

$f-f_1=\frac{f_2-f_1}{x_2-x_1} (x-x_1)\\\\f-20=\frac{32-20}{3-1} (x-1)\\\\f(x)=6x+14$

The flat fee that the store charges is $14

The reasonable domain is 1 ≤ x ≤ 12

The cost for 7 hours is:

f(7) = 6(7) + 14 = 46

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