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The possible inputs of the function is given by the domain of the function
The function that defines the sequence with domain n = {1, 2, 3, 4, 5} is option A. <u>f(n) = -2·n + 10</u>
The given sequence is 8, 6, 4, 2, 0
The required domain of the function is n = {1, 2, 3, 4, 5}
Required:
The function having the given domain that defines the sequence
Solution:
The range of the sequence is f(n) = {8, 6, 4, 2, 0}
Therefore;
f(1) = 8, f(2) = 6, ...f(5) = 0
The first difference of the domain and the range are constant therefore the relationship is linear
The rate of change (slope) of the domain and range is given as follows;
The function relating the range, f(n), to the domain, <em>n</em>, in point and slope form is therefore;
f(n) - 8 = -2· (n - 1)
f(n) = -2·n + 2 + 8
The function in slope and intercept form is; f(n) = -2·n + 10
Therefore;
The function relating the range, f(n), to the domain, <em>n </em>is<u> f(n) = -2·n + 10</u>
The correct option is option A
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