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$Three points on the graph of the function f(x) are {(0,2),(1,4),(2,8)}. Which equation represents f(x) ? f(x)=x^(2)+2 f(x)=2(2)^(x) f(x)=2x+2 f(x)=4x$

Three points on the graph of the function $f(x)$ are $\{(0,2),(1,4),(2,8)\}$ . Which equation represents $f(x)$ ? $\newline$ $f(x)=x^{2}+2$ $\newline$ $f(x)=2(2)^{x}$ $\newline$ $f(x)=2 x+2$ $\newline$ $f(x)=4 x$

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Calculus

Find derivatives of sine and cosine functions

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Q. Three points on the graph of the function

f(x)

are

\{(0,2),(1,4),(2,8)\}

. Which equation represents

f(x)

\newline

f(x)=x^{2}+2

\newline

f(x)=2(2)^{x}

\newline

f(x)=2 x+2

\newline

f(x)=4 x

Test Function with Point $(0, 2)$ : Let's test each given function with the points provided to see which one fits all three points. $\newline$ First, we will test the point $(0, 2)$ with the function $f(x) = x^2 + 2$ . $\newline$ $f(0) = 0^2 + 2 = 2$ . $\newline$ This matches the given point $(0, 2)$ .
Test Function with Point $1, 4$ : Now, let's test the point $1, 4$ with the function $f(x) = x^2 + 2$ . $f(1) = 1^2 + 2 = 1 + 2 = 3.$ This does not match the given point $1, 4$ , so $f(x) = x^2 + 2$ cannot be the correct function.