Let's evaluate $g(x) = \left( \frac{1}{5} \right)^x$ for each given $x$-value.

Step-by-Step Calculations:

1. For $x = -2$: $g(-2) = \left( \frac{1}{5} \right)^{-2} = \frac{1}{\left( \frac{1}{5} \right)^2} = \frac{1}{\frac{1}{25}} = 25$ So, $g(-2) = 25$.

2. For $x = -1$: $g(-1) = \left( \frac{1}{5} \right)^{-1} = \frac{1}{\frac{1}{5}} = 5$ So, $g(-1) = 5$.

3. For $x = 0$: $g(0) = \left( \frac{1}{5} \right)^0 = 1$ So, $g(0) = 1$.

4. For $x = 1$: $g(1) = \left( \frac{1}{5} \right)^1 = \frac{1}{5}$ So, $g(1) = \frac{1}{5}$.

5. For $x = 2$: $g(2) = \left( \frac{1}{5} \right)^2 = \frac{1}{25}$ So, $g(2) = \frac{1}{25}$.

Final Table:

Would you like more details on these calculations or have any other questions?

Here are five related questions for further exploration:

1. How does the behavior of the function $g(x) = \left( \frac{1}{5} \right)^x$ change as $x$ becomes more negative?
2. What would happen if we replaced $\frac{1}{5}$ with a different fraction?
3. How do you interpret negative exponents in terms of reciprocal values?
4. How can you identify an exponential function and its rate of growth or decay?
5. What is the effect of changing the base in an exponential function?

Tip: Remember that raising a fraction to a negative power results in a reciprocal. This is why $\left( \frac{1}{5} \right)^{-1} = 5$.