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$Three points on the graph of the function f(x) are {(0,3),(1,9),(2,27)}. Which equation represents f(x) ? f(x)=3(3)^(x) f(x)=18 x-9 f(x)=x^(2)+3 f(x)=6x+3$

Three points on the graph of the function $f(x)$ are $\{(0,3),(1,9),(2,27)\}$ . Which equation represents $f(x)$ ? $\newline$ $f(x)=3(3)^{x}$ $\newline$ $f(x)=18 x-9$ $\newline$ $f(x)=x^{2}+3$ $\newline$ $f(x)=6 x+3$

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Write a quadratic function from its x-intercepts and another point

Full solution

Q. Three points on the graph of the function

f(x)

are

\{(0,3),(1,9),(2,27)\}

. Which equation represents

f(x)

?

\newline

f(x)=3(3)^{x}

\newline

f(x)=18 x-9

\newline

f(x)=x^{2}+3

\newline

f(x)=6 x+3

Test Function with $(0,3)$ : Test each given function with the first point $(0,3)$ . $\newline$ Substitute $x = 0$ into each function and check if the output is $3$ . $\newline$ For $f(x) = 3(3)^x$ , when $x = 0$ , $f(x) = 3(3)^0 = 3(1) = 3$ .
Test Function with $(1,9)$ : Test each remaining function with the second point $(1,9)$ . $\newline$ Substitute $x = 1$ into each function and check if the output is $9$ . $\newline$ For $f(x) = 3(3)^x$ , when $x = 1$ , $f(x) = 3(3)^1 = 3(3) = 9$ .
Test Function with $(2,27)$ : Test each remaining function with the third point $(2,27)$ . $\newline$ Substitute $x = 2$ into each function and check if the output is $27$ . $\newline$ For $f(x) = 3(3)^x$ , when $x = 2$ , $f(x) = 3(3)^2 = 3(9) = 27$ .

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