Three points on the graph of the function f(x) are {(0,2),(1,3),(2,4)}. Which equation represents f(x) ? f(x)=x^(2)+2 f(x)=x-2 f(x)=2*((3)/(2))^(x) f(x)=x+2

Question

Three points on the graph of the function  f(x) are  {(0,2),(1,3),(2,4)}. Which equation represents  f(x) ?  f(x)=x^(2)+2  f(x)=x-2  f(x)=2*((3)/(2))^(x)  f(x)=x+2

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Test Equation f(x): Test the first equation f(x) = x^2 + 2 with the given points. For (0,2), f(0) = 0^2 + 2 = 2. For (1,3), f(1) = 1^2 + 2 = 3. For (2,4), f(2) = 2^2 + 2 = 6. Check if the calculated values match the given points.Check Calculated Values: Since f(2) = 6 does not match the given point (2,4), the first equation f(x) = x^2 + 2 is not the correct representation of f(x).Test Equation f(x): Test the second equation f(x) = x - 2 with the given points. For (0,2), f(0) = 0 - 2 = -2. For (1,3), f(1) = 1 - 2 = -1. For (2,4), f(2) = 2 - 2 = 0. Check if the calculated values match the given points.Check Calculated Values: Since f(0) = -2 does not match the given point (0,2), the second equation f(x) = x - 2 is not the correct representation of f(x).Test Equation f(x): Test the third equation f(x) = 2 * (3/2)^x with the given points. For (0,2), f(0) = 2 * (3/2)^0 = 2 * 1 = 2. For (1,3), f(1) = 2 * (3/2)^1 = 2 * 3/2 = 3. For (2,4), f(2) = 2 * (3/2)^2 = 2 * 9/4 = 9/2. Check if the calculated values match the given points.

Three points on the graph of the function $f(x)$ are $\{(0,2),(1,3),(2,4)\}$ . Which equation represents $f(x)$ ? $\newline$ $f(x)=x^{2}+2$ $\newline$ $f(x)=x-2$ $\newline$ $f(x)=2 \cdot\left(\frac{3}{2}\right)^{x}$ $\newline$ $f(x)=x+2$

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