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$Three points on the graph of the function f(x) are {(0,2),(1,4),(2,6)}. Which equation represents f(x) ? f(x)=x^(2)+2 f(x)=2x+4 f(x)=2*2^(x) f(x)=2x+2$

Three points on the graph of the function $f(x)$ are $\{(0,2),(1,4),(2,6)\}$ . Which equation represents $f(x)$ ? $\newline$ $f(x)=x^{2}+2$ $\newline$ $f(x)=2 x+4$ $\newline$ $f(x)=2 \cdot 2^{x}$ $\newline$ $f(x)=2 x+2$

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Math Problems

Algebra 1

Compare linear and exponential growth

Full solution

Q. Three points on the graph of the function

f(x)

are

\{(0,2),(1,4),(2,6)\}

. Which equation represents

f(x)

\newline

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

\newline

f(x)=2 x+4

\newline

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

\newline

f(x)=2 x+2

Test Function $(0,2)$ : We will test each given function with the points provided to see which one matches all the points. $\newline$ First, let's test the point $(0,2)$ with each function.
Test Function $(1,4)$ : Testing $f(x) = x^2 + 2$ with $(0,2)$ : $\newline$ $f(0) = 0^2 + 2 = 2$ . $\newline$ This matches the point $(0,2)$ .
Test Function $2,6$ : Testing $f(x) = 2x + 4$ with $0,2$ : $f(0) = 2\cdot 0 + 4 = 4.$ This does not match the point $0,2$ . We can stop considering this function.
Test Function $(2,6)$ : Testing $f(x) = 2x + 4$ with $(0,2)$ :
$f(0) = 2\cdot0 + 4 = 4$ .
This does not match the point $(0,2)$ .
We can stop considering this function.Testing $f(x) = 2\cdot2^x$ with $(0,2)$ :
$f(0) = 2\cdot2^0 = 2\cdot1 = 2$ .
This matches the point $(0,2)$ .
Test Function ( $2$ , $6$ ): Testing $f(x) = 2x + 4$ with $(0,2)$ :
$f(0) = 2\cdot0 + 4 = 4$ .
This does not match the point $(0,2)$ .
We can stop considering this function.Testing $f(x) = 2\cdot2^x$ with $(0,2)$ :
$f(0) = 2\cdot2^0 = 2\cdot1 = 2$ .
This matches the point $(0,2)$ .Testing $f(x) = 2x + 2$ with $(0,2)$ :
$(0,2)$ $0$ .
This matches the point $(0,2)$ .
Test Function ( $2$ , $6$ ): Testing $f(x) = 2x + 4$ with $(0,2)$ :
$f(0) = 2\cdot0 + 4 = 4$ .
This does not match the point $(0,2)$ .
We can stop considering this function.Testing $f(x) = 2\cdot2^x$ with $(0,2)$ :
$f(0) = 2\cdot2^0 = 2\cdot1 = 2$ .
This matches the point $(0,2)$ .Testing $f(x) = 2x + 2$ with $(0,2)$ :
$(0,2)$ $0$ .
This matches the point $(0,2)$ .Now let's test the point $(0,2)$ $2$ with the remaining functions that matched the first point.
Test Function ( $2$ , $6$ ): Testing $f(x) = 2x + 4$ with $(0,2)$ :
$f(0) = 2\cdot0 + 4 = 4$ .
This does not match the point $(0,2)$ .
We can stop considering this function.Testing $f(x) = 2\cdot2^x$ with $(0,2)$ :
$f(0) = 2\cdot2^0 = 2\cdot1 = 2$ .
This matches the point $(0,2)$ .Testing $f(x) = 2x + 2$ with $(0,2)$ :
$(0,2)$ $0$ .
This matches the point $(0,2)$ .Now let's test the point $(0,2)$ $2$ with the remaining functions that matched the first point.Testing $(0,2)$ $3$ with $(0,2)$ $2$ :
$(0,2)$ $5$ .
This does not match the point $(0,2)$ $2$ .
We can stop considering this function.
Test Function ( $2$ , $6$ ): Testing $f(x) = 2x + 4$ with $(0,2)$ :
$f(0) = 2\cdot0 + 4 = 4$ .
This does not match the point $(0,2)$ .
We can stop considering this function.Testing $f(x) = 2\cdot2^x$ with $(0,2)$ :
$f(0) = 2\cdot2^0 = 2\cdot1 = 2$ .
This matches the point $(0,2)$ .Testing $f(x) = 2x + 2$ with $(0,2)$ :
$(0,2)$ $0$ .
This matches the point $(0,2)$ .Now let's test the point $(0,2)$ $2$ with the remaining functions that matched the first point.Testing $(0,2)$ $3$ with $(0,2)$ $2$ :
$(0,2)$ $5$ .
This does not match the point $(0,2)$ $2$ .
We can stop considering this function.Testing $f(x) = 2\cdot2^x$ with $(0,2)$ $2$ :
$(0,2)$ $9$ .
This matches the point $(0,2)$ $2$ .
Test Function ( $2$ , $6$ ): Testing $f(x) = 2x + 4$ with $(0,2)$ :
$f(0) = 2\cdot0 + 4 = 4$ .
This does not match the point $(0,2)$ .
We can stop considering this function.Testing $f(x) = 2\cdot2^x$ with $(0,2)$ :
$f(0) = 2\cdot2^0 = 2\cdot1 = 2$ .
This matches the point $(0,2)$ .Testing $f(x) = 2x + 2$ with $(0,2)$ :
$(0,2)$ $0$ .
This matches the point $(0,2)$ .Now let's test the point $(0,2)$ $2$ with the remaining functions that matched the first point.Testing $(0,2)$ $3$ with $(0,2)$ $2$ :
$(0,2)$ $5$ .
This does not match the point $(0,2)$ $2$ .
We can stop considering this function.Testing $f(x) = 2\cdot2^x$ with $(0,2)$ $2$ :
$(0,2)$ $9$ .
This matches the point $(0,2)$ $2$ .Testing $f(x) = 2x + 2$ with $(0,2)$ $2$ :
$f(0) = 2\cdot0 + 4 = 4$ $3$ .
This matches the point $(0,2)$ $2$ .
Test Function ( $2$ , $6$ ): Testing $f(x) = 2x + 4$ with $(0,2)$ :
$f(0) = 2\cdot0 + 4 = 4$ .
This does not match the point $(0,2)$ .
We can stop considering this function.Testing $f(x) = 2\cdot2^x$ with $(0,2)$ :
$f(0) = 2\cdot2^0 = 2\cdot1 = 2$ .
This matches the point $(0,2)$ .Testing $f(x) = 2x + 2$ with $(0,2)$ :
$(0,2)$ $0$ .
This matches the point $(0,2)$ .Now let's test the point $(0,2)$ $2$ with the remaining functions that matched the first point.Testing $(0,2)$ $3$ with $(0,2)$ $2$ :
$(0,2)$ $5$ .
This does not match the point $(0,2)$ $2$ .
We can stop considering this function.Testing $f(x) = 2\cdot2^x$ with $(0,2)$ $2$ :
$(0,2)$ $9$ .
This matches the point $(0,2)$ $2$ .Testing $f(x) = 2x + 2$ with $(0,2)$ $2$ :
$f(0) = 2\cdot0 + 4 = 4$ $3$ .
This matches the point $(0,2)$ $2$ .Finally, let's test the point $f(0) = 2\cdot0 + 4 = 4$ $5$ with the remaining functions that matched the first two points.
Test Function ( $2$ , $6$ ): Testing $f(x) = 2x + 4$ with $(0,2)$ :
$f(0) = 2\cdot0 + 4 = 4$ .
This does not match the point $(0,2)$ .
We can stop considering this function.Testing $f(x) = 2\cdot2^x$ with $(0,2)$ :
$f(0) = 2\cdot2^0 = 2\cdot1 = 2$ .
This matches the point $(0,2)$ .Testing $f(x) = 2x + 2$ with $(0,2)$ :
$(0,2)$ $0$ .
This matches the point $(0,2)$ .Now let's test the point $(0,2)$ $2$ with the remaining functions that matched the first point.Testing $(0,2)$ $3$ with $(0,2)$ $2$ :
$(0,2)$ $5$ .
This does not match the point $(0,2)$ $2$ .
We can stop considering this function.Testing $f(x) = 2\cdot2^x$ with $(0,2)$ $2$ :
$(0,2)$ $9$ .
This matches the point $(0,2)$ $2$ .Testing $f(x) = 2x + 2$ with $(0,2)$ $2$ :
$f(0) = 2\cdot0 + 4 = 4$ $3$ .
This matches the point $(0,2)$ $2$ .Finally, let's test the point $f(0) = 2\cdot0 + 4 = 4$ $5$ with the remaining functions that matched the first two points.Testing $f(x) = 2\cdot2^x$ with $f(0) = 2\cdot0 + 4 = 4$ $5$ :
$f(0) = 2\cdot0 + 4 = 4$ $8$ .
This does not match the point $f(0) = 2\cdot0 + 4 = 4$ $5$ .
We can stop considering this function.
Test Function ( $2$ , $6$ ): Testing $f(x) = 2x + 4$ with $(0,2)$ :
$f(0) = 2\cdot0 + 4 = 4$ .
This does not match the point $(0,2)$ .
We can stop considering this function.Testing $f(x) = 2\cdot2^x$ with $(0,2)$ :
$f(0) = 2\cdot2^0 = 2\cdot1 = 2$ .
This matches the point $(0,2)$ .Testing $f(x) = 2x + 2$ with $(0,2)$ :
$(0,2)$ $0$ .
This matches the point $(0,2)$ .Now let's test the point $(0,2)$ $2$ with the remaining functions that matched the first point.Testing $(0,2)$ $3$ with $(0,2)$ $2$ :
$(0,2)$ $5$ .
This does not match the point $(0,2)$ $2$ .
We can stop considering this function.Testing $f(x) = 2\cdot2^x$ with $(0,2)$ $2$ :
$(0,2)$ $9$ .
This matches the point $(0,2)$ $2$ .Testing $f(x) = 2x + 2$ with $(0,2)$ $2$ :
$f(0) = 2\cdot0 + 4 = 4$ $3$ .
This matches the point $(0,2)$ $2$ .Finally, let's test the point $f(0) = 2\cdot0 + 4 = 4$ $5$ with the remaining functions that matched the first two points.Testing $f(x) = 2\cdot2^x$ with $f(0) = 2\cdot0 + 4 = 4$ $5$ :
$f(0) = 2\cdot0 + 4 = 4$ $8$ .
This does not match the point $f(0) = 2\cdot0 + 4 = 4$ $5$ .
We can stop considering this function.Testing $f(x) = 2x + 2$ with $f(0) = 2\cdot0 + 4 = 4$ $5$ :
$(0,2)$ $2$ .
This matches the point $f(0) = 2\cdot0 + 4 = 4$ $5$ .
Test Function ( $2$ , $6$ ): Testing $f(x) = 2x + 4$ with $(0,2)$ :
$f(0) = 2\cdot0 + 4 = 4$ .
This does not match the point $(0,2)$ .
We can stop considering this function.
Testing $f(x) = 2\cdot2^x$ with $(0,2)$ :
$f(0) = 2\cdot2^0 = 2\cdot1 = 2$ .
This matches the point $(0,2)$ .
Testing $f(x) = 2x + 2$ with $(0,2)$ :
$(0,2)$ $0$ .
This matches the point $(0,2)$ .
Now let's test the point $(0,2)$ $2$ with the remaining functions that matched the first point.
Testing $(0,2)$ $3$ with $(0,2)$ $2$ :
$(0,2)$ $5$ .
This does not match the point $(0,2)$ $2$ .
We can stop considering this function.
Testing $f(x) = 2\cdot2^x$ with $(0,2)$ $2$ :
$(0,2)$ $9$ .
This matches the point $(0,2)$ $2$ .
Testing $f(x) = 2x + 2$ with $(0,2)$ $2$ :
$f(0) = 2\cdot0 + 4 = 4$ $3$ .
This matches the point $(0,2)$ $2$ .
Finally, let's test the point $f(0) = 2\cdot0 + 4 = 4$ $5$ with the remaining functions that matched the first two points.
Testing $f(x) = 2\cdot2^x$ with $f(0) = 2\cdot0 + 4 = 4$ $5$ :
$f(0) = 2\cdot0 + 4 = 4$ $8$ .
This does not match the point $f(0) = 2\cdot0 + 4 = 4$ $5$ .
We can stop considering this function.
Testing $f(x) = 2x + 2$ with $f(0) = 2\cdot0 + 4 = 4$ $5$ :
$(0,2)$ $2$ .
This matches the point $f(0) = 2\cdot0 + 4 = 4$ $5$ .
Since the function $f(x) = 2x + 2$ is the only function that matches all three points, this is the equation that represents $(0,2)$ $5$ .