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Answer:
i) exponential; values have a common ratio; f(x) = -2·4^x
ii) linear; values have a common difference; f(x) = 4x -3
iii) exponential; values have a common ratio; f(x) = 4·2^x
Step-by-step explanation:
Sequential, or evenly-spaced, input values will result in output values with a common difference if the function is linear. They will result in output values with a common ratio of the function is exponential.
The initial value, or y-intercept, is the value when x=0. The general form of the formulas is ...
linear: f(x) = (common difference)·x + (initial value)
exponential: f(x) = (initial value)·(common ratio)^x
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i) The f(x) values have a common ratio of -8/-2 = 4, so the relation is exponential. The initial value is f(0) = -2. The equation is ...
f(x) = -2·4^x
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ii) The f(x) values have a common difference of 1 -(-3) = 4, so the relation is linear. The initial value is f(0) = -3. The equation is ...
f(x) = 4x -3
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iii) The f(x) values have a common ratio of 8/4 = 2, so the relation is exponential. The initial value is f(0) = 4. The equation is ...
f(x) = 4·2^x
