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$Three points on the graph of the function f(x) are {(0,1),(1,2),(2,5)}. Which equation represents f(x) ? f(x)=x^(2)+1 f(x)=2^(x) f(x)=3x-1 f(x)=x+1$

Three points on the graph of the function $f(x)$ are $\{(0,1),(1,2),(2,5)\}$ . Which equation represents $f(x)$ ? $\newline$ $f(x)=x^{2}+1$ $\newline$ $f(x)=2^{x}$ $\newline$ $f(x)=3 x-1$ $\newline$ $f(x)=x+1$

Full solution

Q. Three points on the graph of the function

f(x)

are

\{(0,1),(1,2),(2,5)\}

. Which equation represents

f(x)

\newline

f(x)=x^{2}+1

\newline

f(x)=2^{x}

\newline

f(x)=3 x-1

\newline

f(x)=x+1

Test Equation with Points: Test the first equation $f(x) = x^2 + 1$ with the given points. $\newline$ For $(0,1)$ : $f(0) = 0^2 + 1 = 1$ . This matches the given point. $\newline$ For $(1,2)$ : $f(1) = 1^2 + 1 = 2$ . This matches the given point. $\newline$ For $(2,5)$ : $f(2) = 2^2 + 1 = 5$ . This matches the given point. $\newline$ All three points match the equation $f(x) = x^2 + 1$ .
Verify Matching Points: Since all points match the first equation, there is no need to test the other equations. We have found the correct equation that represents $f(x)$ .