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

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

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Math Problems

Calculus

Find derivatives of sine and cosine functions

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)=2 \cdot 2^{x}

\newline

f(x)=2 x+2

\newline

f(x)=\frac{1}{2} x-1

\newline

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

Test Function $0, 2$ : Let's test each given function with the points provided to see which one fits all three points. $\newline$ First, we will test the point $0, 2$ with each function.
Test Function ( $1$ , $4$ ): Testing the first function $f(x) = 2 \cdot 2^{x}$ with the point $(0, 2)$ : $f(0) = 2 \cdot 2^{0} = 2 \cdot 1 = 2$ . This matches the y-value of the point $(0, 2)$ .
Test Function ( $2$ , $6$ ): Testing the second function $f(x) = 2x + 2$ with the point $(0, 2)$ : $f(0) = 2\cdot0 + 2 = 0 + 2 = 2.$ This also matches the y-value of the point $(0, 2)$ .
Test Function ( $2$ , $6$ ): Testing the second function $f(x) = 2x + 2$ with the point $(0, 2)$ : $f(0) = 2\cdot 0 + 2 = 0 + 2 = 2.$ This also matches the y-value of the point $(0, 2)$ .Testing the third function $f(x) = \frac{1}{2}x - 1$ with the point $(0, 2)$ : $f(0) = \frac{1}{2}\cdot 0 - 1 = 0 - 1 = -1.$ This does not match the y-value of the point $(0, 2)$ . We can eliminate this function.
Test Function ( $2$ , $6$ ): Testing the second function $f(x) = 2x + 2$ with the point $(0, 2)$ :
$f(0) = 2\cdot0 + 2 = 0 + 2 = 2$ .
This also matches the y-value of the point $(0, 2)$ .Testing the third function $f(x) = \frac{1}{2}x - 1$ with the point $(0, 2)$ :
$f(0) = \frac{1}{2}\cdot0 - 1 = 0 - 1 = -1$ .
This does not match the y-value of the point $(0, 2)$ . We can eliminate this function.Testing the fourth function $f(x) = x^2 + 2$ with the point $(0, 2)$ :
$(0, 2)$ $0$ .
This matches the y-value of the point $(0, 2)$ .
Test Function ( $2$ , $6$ ): Testing the second function $f(x) = 2x + 2$ with the point $(0, 2)$ :
$f(0) = 2\cdot0 + 2 = 0 + 2 = 2$ .
This also matches the y-value of the point $(0, 2)$ .Testing the third function $f(x) = (\frac{1}{2})x - 1$ with the point $(0, 2)$ :
$f(0) = (\frac{1}{2})\cdot0 - 1 = 0 - 1 = -1$ .
This does not match the y-value of the point $(0, 2)$ . We can eliminate this function.Testing the fourth function $f(x) = x^2 + 2$ with the point $(0, 2)$ :
$(0, 2)$ $0$ .
This matches the y-value of the point $(0, 2)$ .Now, let's test the remaining functions with the second point $(0, 2)$ $2$ .
Test Function $(2, 6)$ : Testing the second function $f(x) = 2x + 2$ with the point $(0, 2)$ : $f(0) = 2\cdot0 + 2 = 0 + 2 = 2$ . This also matches the y-value of the point $(0, 2)$ .Testing the third function $f(x) = \frac{1}{2}x - 1$ with the point $(0, 2)$ : $f(0) = \frac{1}{2}\cdot0 - 1 = 0 - 1 = -1$ . This does not match the y-value of the point $(0, 2)$ . We can eliminate this function.Testing the fourth function $f(x) = x^2 + 2$ with the point $(0, 2)$ : $f(x) = 2x + 2$ $1$ . This matches the y-value of the point $(0, 2)$ .Now, let's test the remaining functions with the second point $f(x) = 2x + 2$ $3$ .Testing the first function $f(x) = 2x + 2$ $4$ with the point $f(x) = 2x + 2$ $3$ : $f(x) = 2x + 2$ $6$ . This matches the y-value of the point $f(x) = 2x + 2$ $3$ .
Test Function ( $2$ , $6$ ): Testing the second function $f(x) = 2x + 2$ with the point $(0, 2)$ : $f(0) = 2\cdot 0 + 2 = 0 + 2 = 2.$ This also matches the y-value of the point $(0, 2)$ .Testing the third function $f(x) = \frac{1}{2}x - 1$ with the point $(0, 2)$ : $f(0) = \frac{1}{2}\cdot 0 - 1 = 0 - 1 = -1.$ This does not match the y-value of the point $(0, 2)$ . We can eliminate this function.Testing the fourth function $f(x) = x^2 + 2$ with the point $(0, 2)$ : $f(0) = 0^2 + 2 = 0 + 2 = 2.$ This matches the y-value of the point $(0, 2)$ .Now, let's test the remaining functions with the second point $(1, 4)$ .Testing the first function $(0, 2)$ $0$ with the point $(1, 4)$ : $f(1) = 2\cdot 2^{1} = 2\cdot 2 = 4.$ This matches the y-value of the point $(1, 4)$ .Testing the second function $f(x) = 2x + 2$ with the point $(1, 4)$ : $f(1) = 2\cdot 1 + 2 = 2 + 2 = 4.$ This also matches the y-value of the point $(1, 4)$ .
Test Function ( $2$ , $6$ ): Testing the second function $f(x) = 2x + 2$ with the point $(0, 2)$ :
$f(0) = 2\cdot0 + 2 = 0 + 2 = 2$ .
This also matches the y-value of the point $(0, 2)$ .Testing the third function $f(x) = \frac{1}{2}x - 1$ with the point $(0, 2)$ :
$f(0) = \frac{1}{2}\cdot0 - 1 = 0 - 1 = -1$ .
This does not match the y-value of the point $(0, 2)$ . We can eliminate this function.Testing the fourth function $f(x) = x^2 + 2$ with the point $(0, 2)$ :
$(0, 2)$ $0$ .
This matches the y-value of the point $(0, 2)$ .Now, let's test the remaining functions with the second point $(0, 2)$ $2$ .Testing the first function $(0, 2)$ $3$ with the point $(0, 2)$ $2$ :
$(0, 2)$ $5$ .
This matches the y-value of the point $(0, 2)$ $2$ .Testing the second function $f(x) = 2x + 2$ with the point $(0, 2)$ $2$ :
$(0, 2)$ $9$ .
This also matches the y-value of the point $(0, 2)$ $2$ .Testing the fourth function $f(x) = x^2 + 2$ with the point $(0, 2)$ $2$ :
$f(0) = 2\cdot0 + 2 = 0 + 2 = 2$ $3$ .
This does not match the y-value of the point $(0, 2)$ $2$ . We can eliminate this function.
Test Function ( $2$ , $6$ ): Testing the second function $f(x) = 2x + 2$ with the point $(0, 2)$ :
$f(0) = 2\cdot0 + 2 = 0 + 2 = 2$ .
This also matches the y-value of the point $(0, 2)$ .Testing the third function $f(x) = \frac{1}{2}x - 1$ with the point $(0, 2)$ :
$f(0) = \frac{1}{2}\cdot0 - 1 = 0 - 1 = -1$ .
This does not match the y-value of the point $(0, 2)$ . We can eliminate this function.Testing the fourth function $f(x) = x^2 + 2$ with the point $(0, 2)$ :
$(0, 2)$ $0$ .
This matches the y-value of the point $(0, 2)$ .Now, let's test the remaining functions with the second point $(0, 2)$ $2$ .Testing the first function $(0, 2)$ $3$ with the point $(0, 2)$ $2$ :
$(0, 2)$ $5$ .
This matches the y-value of the point $(0, 2)$ $2$ .Testing the second function $f(x) = 2x + 2$ with the point $(0, 2)$ $2$ :
$(0, 2)$ $9$ .
This also matches the y-value of the point $(0, 2)$ $2$ .Testing the fourth function $f(x) = x^2 + 2$ with the point $(0, 2)$ $2$ :
$f(0) = 2\cdot0 + 2 = 0 + 2 = 2$ $3$ .
This does not match the y-value of the point $(0, 2)$ $2$ . We can eliminate this function.Finally, let's test the remaining functions with the third point $f(0) = 2\cdot0 + 2 = 0 + 2 = 2$ $5$ .
Test Function ( $2$ , $6$ ): Testing the second function $f(x) = 2x + 2$ with the point $(0, 2)$ :
$f(0) = 2\cdot0 + 2 = 0 + 2 = 2$ .
This also matches the y-value of the point $(0, 2)$ .Testing the third function $f(x) = \frac{1}{2}x - 1$ with the point $(0, 2)$ :
$f(0) = \frac{1}{2}\cdot0 - 1 = 0 - 1 = -1$ .
This does not match the y-value of the point $(0, 2)$ . We can eliminate this function.Testing the fourth function $f(x) = x^2 + 2$ with the point $(0, 2)$ :
$(0, 2)$ $0$ .
This matches the y-value of the point $(0, 2)$ .Now, let's test the remaining functions with the second point $(0, 2)$ $2$ .Testing the first function $(0, 2)$ $3$ with the point $(0, 2)$ $2$ :
$(0, 2)$ $5$ .
This matches the y-value of the point $(0, 2)$ $2$ .Testing the second function $f(x) = 2x + 2$ with the point $(0, 2)$ $2$ :
$(0, 2)$ $9$ .
This also matches the y-value of the point $(0, 2)$ $2$ .Testing the fourth function $f(x) = x^2 + 2$ with the point $(0, 2)$ $2$ :
$f(0) = 2\cdot0 + 2 = 0 + 2 = 2$ $3$ .
This does not match the y-value of the point $(0, 2)$ $2$ . We can eliminate this function.Finally, let's test the remaining functions with the third point $f(0) = 2\cdot0 + 2 = 0 + 2 = 2$ $5$ .Testing the first function $(0, 2)$ $3$ with the point $f(0) = 2\cdot0 + 2 = 0 + 2 = 2$ $5$ :
$f(0) = 2\cdot0 + 2 = 0 + 2 = 2$ $8$ .
This does not match the y-value of the point $f(0) = 2\cdot0 + 2 = 0 + 2 = 2$ $5$ . We can eliminate this function.
Test Function ( $2$ , $6$ ): Testing the second function $f(x) = 2x + 2$ with the point $(0, 2)$ :
$f(0) = 2\cdot0 + 2 = 0 + 2 = 2$ .
This also matches the y-value of the point $(0, 2)$ .Testing the third function $f(x) = \frac{1}{2}x - 1$ with the point $(0, 2)$ :
$f(0) = \frac{1}{2}\cdot0 - 1 = 0 - 1 = -1$ .
This does not match the y-value of the point $(0, 2)$ . We can eliminate this function.Testing the fourth function $f(x) = x^2 + 2$ with the point $(0, 2)$ :
$(0, 2)$ $0$ .
This matches the y-value of the point $(0, 2)$ .Now, let's test the remaining functions with the second point $(0, 2)$ $2$ .Testing the first function $(0, 2)$ $3$ with the point $(0, 2)$ $2$ :
$(0, 2)$ $5$ .
This matches the y-value of the point $(0, 2)$ $2$ .Testing the second function $f(x) = 2x + 2$ with the point $(0, 2)$ $2$ :
$(0, 2)$ $9$ .
This also matches the y-value of the point $(0, 2)$ $2$ .Testing the fourth function $f(x) = x^2 + 2$ with the point $(0, 2)$ $2$ :
$f(0) = 2\cdot0 + 2 = 0 + 2 = 2$ $3$ .
This does not match the y-value of the point $(0, 2)$ $2$ . We can eliminate this function.Finally, let's test the remaining functions with the third point $f(0) = 2\cdot0 + 2 = 0 + 2 = 2$ $5$ .Testing the first function $(0, 2)$ $3$ with the point $f(0) = 2\cdot0 + 2 = 0 + 2 = 2$ $5$ :
$f(0) = 2\cdot0 + 2 = 0 + 2 = 2$ $8$ .
This does not match the y-value of the point $f(0) = 2\cdot0 + 2 = 0 + 2 = 2$ $5$ . We can eliminate this function.Testing the second function $f(x) = 2x + 2$ with the point $f(0) = 2\cdot0 + 2 = 0 + 2 = 2$ $5$ :
$(0, 2)$ $2$ .
This matches the y-value of the point $f(0) = 2\cdot0 + 2 = 0 + 2 = 2$ $5$ . Since this is the only function that fits all three points, it must be the correct representation of $(0, 2)$ $4$ .

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

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