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

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

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Math Problems

Calculus

Find derivatives of sine and cosine functions

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Q. Three points on the graph of the function

f(x)

are

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

. Which equation represents

f(x)

\newline

f(x)=(x+1)^{2}

\newline

f(x)=2^{x}

\newline

f(x)=2 x

\newline

f(x)=x+1

Test Function $0, 1$ : Let's test each given function with the points provided to see which one fits all the points. $\newline$ First, we will test the point $0, 1$ with each function.
Test Function $(1, 2)$ : Testing $f(x) = (x+1)^{2}$ : $f(0) = (0+1)^{2} = 1^{2} = 1$ . This matches the y-value of the point $(0, 1)$ .
Test Function $2, 4$ : Testing $f(x) = 2^{x}$ : $f(0) = 2^{0} = 1$ . This also matches the y-value of the point $0, 1$ .
Test Function ( $2$ , $4$ ): Testing $f(x) = 2^{x}$ : $f(0) = 2^{0} = 1$ . This also matches the y-value of the point $(0, 1)$ .Testing $f(x) = 2x$ : $f(0) = 2\times 0 = 0$ . This does not match the y-value of the point $(0, 1)$ . We can eliminate this option.
Test Function $(2, 4)$ : Testing $f(x) = 2^{x}$ : $f(0) = 2^{0} = 1$ . This also matches the y-value of the point $(0, 1)$ .Testing $f(x) = 2x$ : $f(0) = 2\cdot 0 = 0$ . This does not match the y-value of the point $(0, 1)$ . We can eliminate this option.Testing $f(x) = x+1$ : $f(0) = 0+1 = 1$ . This matches the y-value of the point $(0, 1)$ .
Test Function ( $2$ , $4$ ): Testing $f(x) = 2^{x}$ : $f(0) = 2^{0} = 1$ .This also matches the y-value of the point $(0, 1)$ .Testing $f(x) = 2x$ : $f(0) = 2\cdot 0 = 0$ .This does not match the y-value of the point $(0, 1)$ . We can eliminate this option.Testing $f(x) = x+1$ : $f(0) = 0+1 = 1$ .This matches the y-value of the point $(0, 1)$ .Now, let's test the point $(1, 2)$ with the remaining functions.
Test Function $(2, 4)$ : Testing $f(x) = 2^{x}$ : $f(0) = 2^{0} = 1$ . This also matches the y-value of the point $(0, 1)$ .Testing $f(x) = 2x$ : $f(0) = 2\cdot0 = 0$ . This does not match the y-value of the point $(0, 1)$ . We can eliminate this option.Testing $f(x) = x+1$ : $f(0) = 0+1 = 1$ . This matches the y-value of the point $(0, 1)$ .Now, let's test the point $f(x) = 2^{x}$ $0$ with the remaining functions.Testing $f(x) = 2^{x}$ $1$ : $f(x) = 2^{x}$ $2$ . This does not match the y-value of the point $f(x) = 2^{x}$ $0$ . We can eliminate this option.
Test Function ( $2$ , $4$ ): Testing $f(x) = 2^{x}$ : $f(0) = 2^{0} = 1$ . This also matches the y-value of the point $(0, 1)$ .Testing $f(x) = 2x$ : $f(0) = 2\cdot0 = 0$ . This does not match the y-value of the point $(0, 1)$ . We can eliminate this option.Testing $f(x) = x+1$ : $f(0) = 0+1 = 1$ . This matches the y-value of the point $(0, 1)$ .Now, let's test the point $(1, 2)$ with the remaining functions.Testing $f(0) = 2^{0} = 1$ $0$ : $f(0) = 2^{0} = 1$ $1$ . This does not match the y-value of the point $(1, 2)$ . We can eliminate this option.Testing $f(x) = 2^{x}$ : $f(0) = 2^{0} = 1$ $4$ . This matches the y-value of the point $(1, 2)$ .
Test Function ( $2$ , $4$ ): Testing $f(x) = 2^{x}$ : $f(0) = 2^{0} = 1$ . This also matches the y-value of the point $(0, 1)$ .Testing $f(x) = 2x$ : $f(0) = 2\cdot 0 = 0$ . This does not match the y-value of the point $(0, 1)$ . We can eliminate this option.Testing $f(x) = x+1$ : $f(0) = 0+1 = 1$ . This matches the y-value of the point $(0, 1)$ .Now, let's test the point $(1, 2)$ with the remaining functions.Testing $f(0) = 2^{0} = 1$ $0$ : $f(0) = 2^{0} = 1$ $1$ . This does not match the y-value of the point $(1, 2)$ . We can eliminate this option.Testing $f(x) = 2^{x}$ : $f(0) = 2^{0} = 1$ $4$ . This matches the y-value of the point $(1, 2)$ .Testing $f(x) = x+1$ : $f(0) = 2^{0} = 1$ $7$ . This matches the y-value of the point $(1, 2)$ .
Test Function ( $2$ , $4$ ): Testing $f(x) = 2^{x}$ : $f(0) = 2^{0} = 1$ .This also matches the y-value of the point $(0, 1)$ .Testing $f(x) = 2x$ : $f(0) = 2\cdot0 = 0$ .This does not match the y-value of the point $(0, 1)$ . We can eliminate this option.Testing $f(x) = x+1$ : $f(0) = 0+1 = 1$ .This matches the y-value of the point $(0, 1)$ .Now, let's test the point $(1, 2)$ with the remaining functions.Testing $f(0) = 2^{0} = 1$ $0$ : $f(0) = 2^{0} = 1$ $1$ .This does not match the y-value of the point $(1, 2)$ . We can eliminate this option.Testing $f(x) = 2^{x}$ : $f(0) = 2^{0} = 1$ $4$ .This matches the y-value of the point $(1, 2)$ .Testing $f(x) = x+1$ : $f(0) = 2^{0} = 1$ $7$ .This matches the y-value of the point $(1, 2)$ .Finally, let's test the point $f(0) = 2^{0} = 1$ $9$ with the remaining functions.
Test Function $(2, 4)$ : Testing $f(x) = 2^{x}$ : $f(0) = 2^{0} = 1$ . This also matches the y-value of the point $(0, 1)$ .Testing $f(x) = 2x$ : $f(0) = 2\cdot 0 = 0$ . This does not match the y-value of the point $(0, 1)$ . We can eliminate this option.Testing $f(x) = x+1$ : $f(0) = 0+1 = 1$ . This matches the y-value of the point $(0, 1)$ .Now, let's test the point $f(x) = 2^{x}$ $0$ with the remaining functions.Testing $f(x) = 2^{x}$ $1$ : $f(x) = 2^{x}$ $2$ . This does not match the y-value of the point $f(x) = 2^{x}$ $0$ . We can eliminate this option.Testing $f(x) = 2^{x}$ : $f(x) = 2^{x}$ $5$ . This matches the y-value of the point $f(x) = 2^{x}$ $0$ .Testing $f(x) = x+1$ : $f(x) = 2^{x}$ $8$ . This matches the y-value of the point $f(x) = 2^{x}$ $0$ .Finally, let's test the point $(2, 4)$ with the remaining functions.Testing $f(x) = 2^{x}$ : $f(0) = 2^{0} = 1$ $2$ . This matches the y-value of the point $(2, 4)$ .
Test Function ( $2$ , $4$ ): Testing $f(x) = 2^{x}$ : $f(0) = 2^{0} = 1$ . This also matches the y-value of the point $(0, 1)$ .Testing $f(x) = 2x$ : $f(0) = 2\cdot0 = 0$ . This does not match the y-value of the point $(0, 1)$ . We can eliminate this option.Testing $f(x) = x+1$ : $f(0) = 0+1 = 1$ . This matches the y-value of the point $(0, 1)$ .Now, let's test the point $(1, 2)$ with the remaining functions.Testing $f(0) = 2^{0} = 1$ $0$ : $f(0) = 2^{0} = 1$ $1$ . This does not match the y-value of the point $(1, 2)$ . We can eliminate this option.Testing $f(x) = 2^{x}$ : $f(0) = 2^{0} = 1$ $4$ . This matches the y-value of the point $(1, 2)$ .Testing $f(x) = x+1$ : $f(0) = 2^{0} = 1$ $7$ . This matches the y-value of the point $(1, 2)$ .Finally, let's test the point $f(0) = 2^{0} = 1$ $9$ with the remaining functions.Testing $f(x) = 2^{x}$ : $(0, 1)$ $1$ . This matches the y-value of the point $f(0) = 2^{0} = 1$ $9$ .Testing $f(x) = x+1$ : $(0, 1)$ $4$ . This does not match the y-value of the point $f(0) = 2^{0} = 1$ $9$ . We can eliminate this option.
Test Function ( $2$ , $4$ ): Testing $f(x) = 2^{x}$ : $f(0) = 2^{0} = 1$ . This also matches the y-value of the point $(0, 1)$ . Testing $f(x) = 2x$ : $f(0) = 2\cdot 0 = 0$ . This does not match the y-value of the point $(0, 1)$ . We can eliminate this option. Testing $f(x) = x+1$ : $f(0) = 0+1 = 1$ . This matches the y-value of the point $(0, 1)$ . Now, let's test the point $(1, 2)$ with the remaining functions. Testing $f(0) = 2^{0} = 1$ $0$ : $f(0) = 2^{0} = 1$ $1$ . This does not match the y-value of the point $(1, 2)$ . We can eliminate this option. Testing $f(x) = 2^{x}$ : $f(0) = 2^{0} = 1$ $4$ . This matches the y-value of the point $(1, 2)$ . Testing $f(x) = x+1$ : $f(0) = 2^{0} = 1$ $7$ . This matches the y-value of the point $(1, 2)$ . Finally, let's test the point $f(0) = 2^{0} = 1$ $9$ with the remaining functions. Testing $f(x) = 2^{x}$ : $(0, 1)$ $1$ . This matches the y-value of the point $f(0) = 2^{0} = 1$ $9$ . Testing $f(x) = x+1$ : $(0, 1)$ $4$ . This does not match the y-value of the point $f(0) = 2^{0} = 1$ $9$ . We can eliminate this option. The only function that matches all the given points is $f(x) = 2^{x}$ .

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

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