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 = <u>[0, 3,650]</u>, R =<u> [20, 9,145]</u>
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 <em>x</em> movies
Required:
The domain and the range of <em>x</em>
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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 =<u> [0, 3650]</u>
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The amount paid for renting <em>x</em> 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, <em>20 ≤ f(x) ≤ 9,145</em>
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- The range of the function is therefore; <u>R = [20, 9145]</u>
The option that gives the domain and the range of the function is therefore;
A. OD = <u>[0, 3,650], R = [20, 9,145]</u>
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