Question

Movie Galore Video Store is open every day of the year. To rent movies from the store, a person has to pay an
annual membership fee of $20, plus $2.50 for each movie rented. To reduce the chance that movies are returned
late, members are not allowed to rent more than 10 movies per day. Billy decides to become a member of the
video store. Let x represent the number of movies that Billy could rent next year, and let f(x) represent the
amount (in dollars) that he would pay the store as a result. Then f(x) is a function of x. What is the domain D and
range R of f(x)?
A OD = [0, 3650], R = [20, 9145]
BOD= [0, 3650), R = [0, 9125]
COD= [0, 365], R = [0, 912.50]
DO D = [0, 365), R = [20, 932.50]

Answer 1

The domain of a function, is the set of the possible input values, while the range is the set of the function's output values

The domain and the range of f(x) is; A. OD = [0, 3,650], R = [20, 9,145]

Reasons:

The given parameters are;

Amount a person has to pay as membership fee = $20

Amount paid for each movie rented = $2.50

Maximum number of movies that can be rented per day = 10 movies

x = Number of movies that can be rented by Billy next year

f(x) = The amount Billy would pay for renting x movies

Required:

The domain and the range of x

Solution:

The number of days in a year, n = 365 days

The maximum number of movies Billy can rent in a year, R = 10·n

Therefore;

R = 10 × 365 = 3,650

Which gives;

The number of films Billy could rent in a year is 0 ≤ x ≤ 3,650

• The domain of the function is OD = [0, 3650]

The amount paid for renting x movies, f(x) = 20 + 2.5·x

From the given domain, we have;

Minimum amount paid, f(0) = 20 + 2.5 × 0 = 20

Maximum amount paid, f(3,650) = 20 + 2.5 × 3,650 = 9,145

The range of the function is therefore, 20 ≤ f(x) ≤ 9,145

• The range of the function is therefore; R = [20, 9145]

The option that gives the domain and the range of the function is therefore;

A. OD = [0, 3,650], R = [20, 9,145]

Learn more here:

https://brainly.com/question/17514387