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

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

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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),(2,9)\}

. Which equation represents

f(x)

\newline

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

\newline

f(x)=\frac{1}{3} x-1

\newline

f(x)=3 x+3

\newline

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

Test Function $0,3$ : We will test each given function with the points provided to see which one matches all three points. $\newline$ First, let's test the point $0,3$ with each function.
Test Functions ( $1$ , $6$ ): Testing $f(x)=3\cdot2^{x}$ with $x=0$ : $f(0)=3\cdot2^{0}=3\cdot1=3$ This matches the point $(0,3)$ .
Test Functions $(2,9)$ : Testing $f(x)=\frac{1}{3}x-1$ with $x=0$ : $f(0)=\frac{1}{3}\cdot 0-1=0-1=-1$ This does not match the point $(0,3)$ . Since this function does not match the first point, it cannot be the correct function.
Test Functions $(2,9)$ : Testing $f(x)=\frac{1}{3}x-1$ with $x=0$ :
$f(0)=\frac{1}{3}\cdot 0-1=0-1=-1$
This does not match the point $(0,3)$ .
Since this function does not match the first point, it cannot be the correct function.Testing $f(x)=3x+3$ with $x=0$ :
$f(0)=3\cdot 0+3=0+3=3$
This matches the point $(0,3)$ .
Test Functions $(2,9)$ : Testing $f(x)=\frac{1}{3}x-1$ with $x=0$ : $\newline$ $f(0)=\frac{1}{3}\cdot 0-1=0-1=-1$ $\newline$ This does not match the point $(0,3)$ . $\newline$ Since this function does not match the first point, it cannot be the correct function.Testing $f(x)=3x+3$ with $x=0$ : $\newline$ $f(0)=3\cdot 0+3=0+3=3$ $\newline$ This matches the point $(0,3)$ .Testing $f(x)=x^{2}+3$ with $x=0$ : $\newline$ $f(x)=\frac{1}{3}x-1$ $1$ $\newline$ This matches the point $(0,3)$ .
Test Functions ( $2$ , $9$ ): Testing $f(x)=\frac{1}{3}x-1$ with $x=0$ :
$f(0)=\frac{1}{3}\cdot0-1=0-1=-1$
This does not match the point $(0,3)$ .
Since this function does not match the first point, it cannot be the correct function.Testing $f(x)=3x+3$ with $x=0$ :
$f(0)=3\cdot0+3=0+3=3$
This matches the point $(0,3)$ .Testing $f(x)=x^{2}+3$ with $x=0$ :
$x=0$ $0$
This matches the point $(0,3)$ .Now let's test the point $x=0$ $2$ with the functions that matched the first point.
Test Functions $(2,9)$ : Testing $f(x)=\frac{1}{3}x-1$ with $x=0$ : $f(0)=\frac{1}{3}\cdot0-1=0-1=-1$ This does not match the point $(0,3)$ .Since this function does not match the first point, it cannot be the correct function.Testing $f(x)=3x+3$ with $x=0$ : $f(0)=3\cdot0+3=0+3=3$ This matches the point $(0,3)$ .Testing $f(x)=x^{2}+3$ with $x=0$ : $f(x)=\frac{1}{3}x-1$ $1$ This matches the point $(0,3)$ .Now let's test the point $f(x)=\frac{1}{3}x-1$ $3$ with the functions that matched the first point.Testing $f(x)=\frac{1}{3}x-1$ $4$ with $f(x)=\frac{1}{3}x-1$ $5$ : $f(x)=\frac{1}{3}x-1$ $6$ This matches the point $f(x)=\frac{1}{3}x-1$ $3$ .
Test Functions $(2,9)$ : Testing $f(x)=\frac{1}{3}x-1$ with $x=0$ : $f(0)=\frac{1}{3}\cdot 0-1=0-1=-1$ This does not match the point $(0,3)$ . Since this function does not match the first point, it cannot be the correct function.Testing $f(x)=3x+3$ with $x=0$ : $f(0)=3\cdot 0+3=0+3=3$ This matches the point $(0,3)$ .Testing $f(x)=x^{2}+3$ with $x=0$ : $f(x)=\frac{1}{3}x-1$ $1$ This matches the point $(0,3)$ .Now let's test the point $f(x)=\frac{1}{3}x-1$ $3$ with the functions that matched the first point.Testing $f(x)=\frac{1}{3}x-1$ $4$ with $f(x)=\frac{1}{3}x-1$ $5$ : $f(x)=\frac{1}{3}x-1$ $6$ This matches the point $f(x)=\frac{1}{3}x-1$ $3$ .Testing $f(x)=3x+3$ with $f(x)=\frac{1}{3}x-1$ $5$ : $x=0$ $0$ This matches the point $f(x)=\frac{1}{3}x-1$ $3$ .
Test Functions $(2,9)$ : Testing $f(x)=\frac{1}{3}x-1$ with $x=0$ : $\newline$ $f(0)=\frac{1}{3}\cdot 0-1=0-1=-1$ $\newline$ This does not match the point $(0,3)$ . $\newline$ Since this function does not match the first point, it cannot be the correct function.Testing $f(x)=3x+3$ with $x=0$ : $\newline$ $f(0)=3\cdot 0+3=0+3=3$ $\newline$ This matches the point $(0,3)$ .Testing $f(x)=x^{2}+3$ with $x=0$ : $\newline$ $f(x)=\frac{1}{3}x-1$ $1$ $\newline$ This matches the point $(0,3)$ .Now let's test the point $f(x)=\frac{1}{3}x-1$ $3$ with the functions that matched the first point.Testing $f(x)=\frac{1}{3}x-1$ $4$ with $f(x)=\frac{1}{3}x-1$ $5$ : $\newline$ $f(x)=\frac{1}{3}x-1$ $6$ $\newline$ This matches the point $f(x)=\frac{1}{3}x-1$ $3$ .Testing $f(x)=3x+3$ with $f(x)=\frac{1}{3}x-1$ $5$ : $\newline$ $x=0$ $0$ $\newline$ This matches the point $f(x)=\frac{1}{3}x-1$ $3$ .Testing $f(x)=x^{2}+3$ with $f(x)=\frac{1}{3}x-1$ $5$ : $\newline$ $x=0$ $4$ $\newline$ This does not match the point $f(x)=\frac{1}{3}x-1$ $3$ . $\newline$ Since this function does not match the second point, it cannot be the correct function.
Test Functions ( $2$ , $9$ ): Testing $f(x)=\frac{1}{3}x-1$ with $x=0$ :
$f(0)=\frac{1}{3}\cdot0-1=0-1=-1$
This does not match the point $(0,3)$ .
Since this function does not match the first point, it cannot be the correct function.Testing $f(x)=3x+3$ with $x=0$ :
$f(0)=3\cdot0+3=0+3=3$
This matches the point $(0,3)$ .Testing $f(x)=x^{2}+3$ with $x=0$ :
$x=0$ $0$
This matches the point $(0,3)$ .Now let's test the point $x=0$ $2$ with the functions that matched the first point.Testing $x=0$ $3$ with $x=0$ $4$ :
$x=0$ $5$
This matches the point $x=0$ $2$ .Testing $f(x)=3x+3$ with $x=0$ $4$ :
$x=0$ $9$
This matches the point $x=0$ $2$ .Testing $f(x)=x^{2}+3$ with $x=0$ $4$ :
$f(0)=\frac{1}{3}\cdot0-1=0-1=-1$ $3$
This does not match the point $x=0$ $2$ .
Since this function does not match the second point, it cannot be the correct function.Finally, let's test the point $f(0)=\frac{1}{3}\cdot0-1=0-1=-1$ $5$ with the functions that matched the first two points.
Test Functions $(2,9)$ : Testing $f(x)=\frac{1}{3}x-1$ with $x=0$ : $\newline$ $f(0)=\frac{1}{3}\cdot 0-1=0-1=-1$ $\newline$ This does not match the point $(0,3)$ . $\newline$ Since this function does not match the first point, it cannot be the correct function.Testing $f(x)=3x+3$ with $x=0$ : $\newline$ $f(0)=3\cdot 0+3=0+3=3$ $\newline$ This matches the point $(0,3)$ .Testing $f(x)=x^{2}+3$ with $x=0$ : $\newline$ $f(x)=\frac{1}{3}x-1$ $1$ $\newline$ This matches the point $(0,3)$ .Now let's test the point $f(x)=\frac{1}{3}x-1$ $3$ with the functions that matched the first point.Testing $f(x)=\frac{1}{3}x-1$ $4$ with $f(x)=\frac{1}{3}x-1$ $5$ : $\newline$ $f(x)=\frac{1}{3}x-1$ $6$ $\newline$ This matches the point $f(x)=\frac{1}{3}x-1$ $3$ .Testing $f(x)=3x+3$ with $f(x)=\frac{1}{3}x-1$ $5$ : $\newline$ $x=0$ $0$ $\newline$ This matches the point $f(x)=\frac{1}{3}x-1$ $3$ .Testing $f(x)=x^{2}+3$ with $f(x)=\frac{1}{3}x-1$ $5$ : $\newline$ $x=0$ $4$ $\newline$ This does not match the point $f(x)=\frac{1}{3}x-1$ $3$ . $\newline$ Since this function does not match the second point, it cannot be the correct function.Finally, let's test the point $(2,9)$ with the functions that matched the first two points.Testing $f(x)=\frac{1}{3}x-1$ $4$ with $x=0$ $8$ : $\newline$ $x=0$ $9$ $\newline$ This does not match the point $(2,9)$ . $\newline$ Since this function does not match the third point, it cannot be the correct function.
Test Functions $(2,9)$ : Testing $f(x)=\frac{1}{3}x-1$ with $x=0$ : $\newline$ $f(0)=\frac{1}{3}\cdot 0-1=0-1=-1$ $\newline$ This does not match the point $(0,3)$ . $\newline$ Since this function does not match the first point, it cannot be the correct function.Testing $f(x)=3x+3$ with $x=0$ : $\newline$ $f(0)=3\cdot 0+3=0+3=3$ $\newline$ This matches the point $(0,3)$ .Testing $f(x)=x^{2}+3$ with $x=0$ : $\newline$ $f(x)=\frac{1}{3}x-1$ $1$ $\newline$ This matches the point $(0,3)$ .Now let's test the point $f(x)=\frac{1}{3}x-1$ $3$ with the functions that matched the first point.Testing $f(x)=\frac{1}{3}x-1$ $4$ with $f(x)=\frac{1}{3}x-1$ $5$ : $\newline$ $f(x)=\frac{1}{3}x-1$ $6$ $\newline$ This matches the point $f(x)=\frac{1}{3}x-1$ $3$ .Testing $f(x)=3x+3$ with $f(x)=\frac{1}{3}x-1$ $5$ : $\newline$ $x=0$ $0$ $\newline$ This matches the point $f(x)=\frac{1}{3}x-1$ $3$ .Testing $f(x)=x^{2}+3$ with $f(x)=\frac{1}{3}x-1$ $5$ : $\newline$ $x=0$ $4$ $\newline$ This does not match the point $f(x)=\frac{1}{3}x-1$ $3$ . $\newline$ Since this function does not match the second point, it cannot be the correct function.Finally, let's test the point $(2,9)$ with the functions that matched the first two points.Testing $f(x)=\frac{1}{3}x-1$ $4$ with $x=0$ $8$ : $\newline$ $x=0$ $9$ $\newline$ This does not match the point $(2,9)$ . $\newline$ Since this function does not match the third point, it cannot be the correct function.Testing $f(x)=3x+3$ with $x=0$ $8$ : $\newline$ $f(0)=\frac{1}{3}\cdot 0-1=0-1=-1$ $3$ $\newline$ This matches the point $(2,9)$ . $\newline$ Since this function matches all three points, it must be the correct function.

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

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