Three points on the graph of the function f(x) are {(0,3),(1,9),(2,27)}. Which equation represents f(x) ?

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Three points on the graph of the function  f(x) are  {(0,3),(1,9),(2,27)}. Which equation represents  f(x) ?

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Observe Pattern: Observe the given points to determine the pattern of the function. The points are (0,3), (1,9), and (2,27). We notice that as x increases by 1, the y-value seems to be multiplied by 3 each time. This suggests an exponential pattern.Test Exponential Function: Test the hypothesis that the function is exponential. If the function is exponential, it could be of the form f(x) = a * b^x. Since f(0) = 3, we can determine the value of a because any number to the power of 0 is 1. So, a * 1 = 3, which means a = 3.Determine Value of a: Use another point to determine the value of b. Using the point (1,9), we substitute x with 1 and f(x) with 9 in the equation f(x) = 3 * b^x. We get 9 = 3 * b^1, which simplifies to b = 9 / 3 = 3.Verify with Third Point: Verify the function with the third point. Using the point (2,27), we substitute x with 2 and f(x) with 27 in the equation f(x) = 3 * 3^x. We get 27 = 3 * 3^2, which simplifies to 27 = 3 * 9 = 27. This confirms our function is correct.

Three points on the graph of the function $f(x)$ are $\{(0,3),(1,9),(2,27)\}$ . Which equation represents $f(x)$ ?

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Three points on the graph of the function f(x) f(x) f(x) are {(0,3),(1,9),(2,27)} \{(0,3),(1,9),(2,27)\} {(0,3),(1,9),(2,27)}. Which equation represents f(x) f(x) f(x) ?

Three points on the graph of the function $f(x)$ are $\{(0,3),(1,9),(2,27)\}$ . Which equation represents $f(x)$ ?