Questions: The function g is defined by the following rule. g(x) = (1/6)^x Find g(x) for each x-value in the table. x g(x) -2 -1 0 1

The function g is defined by the following rule.

g(x) = (1/6)^x

Find g(x) for each x-value in the table.

x  g(x)
-2  
-1  
0  
1
Transcript text: The function $g$ is defined by the following rule. \[ g(x)=\left(\frac{1}{6}\right)^{x} \] Find $g(x)$ for each $x$-value in the table. \begin{tabular}{|c|c|} \hline$x$ & $g(x)$ \\ \hline-2 & $\square$ \\ \hline-1 & $\square$ \\ \hline 0 & $\square$ \\ \hline 1 & $\square$ \\ \hline \end{tabular}
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Solution

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Solution Steps

Step 1: Evaluate \( g(x) \) for \( x = -2 \)

The function \( g(x) \) is given by:

\[ g(x) = \left( \frac{1}{6} \right)^x \]

For \( x = -2 \):

\[ g(-2) = \left( \frac{1}{6} \right)^{-2} = \left( \frac{6}{1} \right)^2 = 6^2 = 36 \]

Step 2: Evaluate \( g(x) \) for \( x = -1 \)

For \( x = -1 \):

\[ g(-1) = \left( \frac{1}{6} \right)^{-1} = \frac{6}{1} = 6 \]

Step 3: Evaluate \( g(x) \) for \( x = 0 \)

For \( x = 0 \):

\[ g(0) = \left( \frac{1}{6} \right)^0 = 1 \]

Final Answer

\[ \begin{array}{|c|c|} \hline x & g(x) \\ \hline -2 & \boxed{36} \\ \hline -1 & \boxed{6} \\ \hline 0 & \boxed{1} \\ \hline \end{array} \]

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