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

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

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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)=6 x

\newline

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

\newline

f(x)=3 x+3

\newline

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

Test Function $1$ : 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 $f(x) = 6x$ . $\newline$ We will substitute $x = 0$ into the function and check if the output is $3$ . $\newline$ $f(0) = 6 \times 0 = 0$
Test Function $2$ : Since $f(0)$ should equal $3$ , but we got $0$ , the first option $f(x) = 6x$ does not fit the given point $(0,3)$ .
Check Function $2$ : Now let's test the second option $f(x) = 3(2)^x$ . $\newline$ Substitute $x = 0$ into the function and check if the output is $3$ . $\newline$ $f(0) = 3 \times (2)^0 = 3 \times 1 = 3$
Check Function $2$ : The second option $f(x) = 3(2)^x$ fits the first point $(0,3)$ . Now let's check the second point $(1,6)$ . $\newline$ Substitute $x = 1$ into the function and check if the output is $6$ . $\newline$ $f(1) = 3 \times (2)^1 = 3 \times 2 = 6$
Final Result: The second option $f(x) = 3(2)^x$ also fits the second point $(1,6)$ . Now let's check the third point $(2,12)$ . $\newline$ Substitute $x = 2$ into the function and check if the output is $12$ . $\newline$ $f(2) = 3 \times (2)^2 = 3 \times 4 = 12$
Final Result: The second option $f(x) = 3(2)^x$ also fits the second point $(1,6)$ . Now let's check the third point $(2,12)$ . Substitute $x = 2$ into the function and check if the output is $12$ . $f(2) = 3 \times (2)^2 = 3 \times 4 = 12$ The second option $f(x) = 3(2)^x$ fits all three points $(0,3), (1,6),$ and $(2,12)$ . Therefore, we have found the correct function that represents $f(x)$ .