Answer:
Step-by-step explanation: To graph the value of the term f(n) as a function of the term n for the first four terms of the sequence, let's start by applying the recursive definition to find the values of f(n).
Using the given recursive definition:
f(0) = 20
f(n) = f(n-1) - 4 for n ≥ 1
Let's calculate the values of f(n) for n = 0, 1, 2, and 3:
For n = 0:
f(0) = 20
For n = 1:
f(1) = f(1-1) - 4 = f(0) - 4 = 20 - 4 = 16
For n = 2:
f(2) = f(2-1) - 4 = f(1) - 4 = 16 - 4 = 12
For n = 3:
f(3) = f(3-1) - 4 = f(2) - 4 = 12 - 4 = 8
Now, let's plot these values on a graph, with the term n on the x-axis and the value of f(n) on the y-axis:
Point A: (0, 20)
Point B: (1, 16)
Point C: (2, 12)
Point D: (3, 8)
To graph these points, slide each point up or down into the correct place:
Point A: (0, 20) ●
Point B: (1, 16) ●
Point C: (2, 12) ●
Point D: (3, 8) ●
Now, connect these points with a line:
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This graph represents the values of the sequence f(n) for the first four terms, with the x-axis representing the term number (n) and the y-axis representing the value of f(n). The line connects the points (0, 20), (1, 16), (2, 12), and (3, 8).