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$Three points on the graph of the function f(x) are {(0,6),(1,7),(2,10)}. Which equation represents f(x) ? f(x)=6*((7)/(6))^(x) f(x)=3x+4 f(x)=x+6 f(x)=x^(2)+6$

Three points on the graph of the function $f(x)$ are $\{(0,6),(1,7),(2,10)\}$ . Which equation represents $f(x)$ ? $\newline$ $f(x)=6 \cdot\left(\frac{7}{6}\right)^{x}$ $\newline$ $f(x)=3 x+4$ $\newline$ $f(x)=x+6$ $\newline$ $f(x)=x^{2}+6$

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Operations with rational exponents

Full solution

Q. Three points on the graph of the function

f(x)

are

\{(0,6),(1,7),(2,10)\}

. Which equation represents

f(x)

?

\newline

f(x)=6 \cdot\left(\frac{7}{6}\right)^{x}

\newline

f(x)=3 x+4

\newline

f(x)=x+6

\newline

f(x)=x^{2}+6

Check Function $1$ : We will test each given function with the points provided to see which one matches all the points. $\newline$ Let's start with the first option: $f(x) = 6 \times \left(\frac{7}{6}\right)^{x}$ . $\newline$ We will plug in $x = 0$ and check if $f(0) = 6$ . $\newline$ $f(0) = 6 \times \left(\frac{7}{6}\right)^{0} = 6 \times 1 = 6$ .
Check Function $1$ : Now we will plug in $x = 1$ and check if $f(1) = 7$ . $\newline$ $f(1) = 6 \times \left(\frac{7}{6}\right)^{1} = 6 \times \left(\frac{7}{6}\right) = 7$ .
Check Function $1$ : Next, we will plug in $x = 2$ and check if $f(2) = 10$ . $f(2) = 6 \times \left(\frac{7}{6}\right)^{2} = 6 \times \left(\frac{49}{36}\right) = \frac{49}{6}$ . $\frac{49}{6}$ does not equal $10$ , so this function does not represent $f(x)$ for all given points.
Check Function $2$ : Let's move on to the second option: $f(x) = 3x + 4$ . $\newline$ We will plug in $x = 0$ and check if $f(0) = 6$ . $\newline$ $f(0) = 3 \times 0 + 4 = 4$ . $\newline$ $4$ does not equal $6$ , so this function does not represent $f(x)$ for all given points.

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