Question

Consider the sequence whose first five terms are shown below.

Answer 1

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. f(n) = -2·n + 10

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;

$Rate \ of \ change = \dfrac{8 - 6}{1-2 } = -2$

The function relating the range, f(n), to the domain, n, 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, n is f(n) = -2·n + 10

The correct option is option A

Learn more here:

brainly.com/question/24592110