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$Three points on the graph of the function f(x) are {(0,3),(1,6),(2,12)}. Which equation represents f(x) ? f(x)=3x+3 f(x)=3(2)^(x) f(x)=x^(2)+3 f(x)=6x$

Three points on the graph of the function $f(x)$ are $\{(0,3),(1,6),(2,12)\}$ . Which equation represents $f(x)$ ? $\newline$ $f(x)=3 x+3$ $\newline$ $f(x)=3(2)^{x}$ $\newline$ $f(x)=x^{2}+3$ $\newline$ $f(x)=6 x$

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Math Problems

Algebra 1

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),(1,6),(2,12)\}

. Which equation represents

f(x)

\newline

f(x)=3 x+3

\newline

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

\newline

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

\newline

f(x)=6 x

Test Function $1$ : $f(x) = 3x + 3$ : We will test each given function with the points provided to see which one fits all three points. $\newline$ Let's start with the first option: $f(x) = 3x + 3$ . $\newline$ We will substitute $x = 0$ into the equation and see if we get $y = 3$ . $\newline$ $f(0) = 3(0) + 3 = 0 + 3 = 3$ . $\newline$ This matches the first point $(0,3)$ .
Test Function $1$ with Point $1,6$ : Now we will test the first equation with the second point $1,6$ . $f(1) = 3(1) + 3 = 3 + 3 = 6.$ This matches the second point $1,6$ .
Test Function $1$ with Point $(2,12)$ : Next, we will test the first equation with the third point $(2,12)$ . $\newline$ $f(2) = 3(2) + 3 = 6 + 3 = 9$ . $\newline$ This does not match the third point $(2,12)$ , so $f(x) = 3x + 3$ is not the correct equation.
Test Function $2$ : $f(x) = 3(2)^x$ : Let's move on to the second option: $f(x) = 3(2)^x$ . We will substitute $x = 0$ into the equation and see if we get $y = 3$ . $f(0) = 3(2)^0 = 3(1) = 3$ . This matches the first point $(0,3)$ .
Test Function $2$ with Point $(1,6)$ : Now we will test the second equation with the second point $(1,6)$ . $\newline$ $f(1) = 3(2)^1 = 3(2) = 6.$ $\newline$ This matches the second point $(1,6)$ .
Test Function $2$ with Point $(2,12)$ : Next, we will test the second equation with the third point $(2,12)$ . $\newline$ $f(2) = 3(2)^2 = 3(4) = 12.$ $\newline$ This matches the third point $(2,12)$ , so $f(x) = 3(2)^x$ is the correct equation.