The rule extracted from the given table is f(n) = 3n; where n is the input. Using the direct variation method, the required rule is extracted.
What is the direct variation method for finding a rule for the table?
The direct variation method is applicable for the table if both the variables(input and output) are direct i.e., their ratio remains a constant for all the values.
Thus, the rule by direct variation method is y = ax or f(x) = ax; where 'a' is the constant - ratio of output to the input.
Calculation:
It is given that,
Input(n): -1, 0, 1, 2, 3, 4
Output(f(n): -3, 0, 3, 6, 9, 12
Since the input and output values are direct, their ratio is a = f(n)/n
⇒ a = -3/-1 = 3
or a = 3/1 = 3; a = 6/2 = 3 ...
So, 'a' remains constant for all the input and outputs from the table.
Then, the rule for the table is
y = ax ⇒ f(n) = an
∴ f(n) = 3n
Thus, the rule for the given table is 'f(n) = 3n'.
Learn more about the direct variation method here:
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