Let's break down the problem step by step based on the given function $g(x) = \left( \frac{1}{2} \right)^x$.

For Part 1, you're asked to evaluate $g(-2)$.

To do so, simply substitute $x = -2$ into the equation:

$g(-2) = \left( \frac{1}{2} \right)^{-2}$

Now, recall the rule of exponents: $a^{-b} = \frac{1}{a^b}$. So,

$g(-2) = \frac{1}{\left( \frac{1}{2} \right)^2} = \frac{1}{\frac{1}{4}} = 4$

Thus, $g(-2) = 4$.

If you'd like, I can help you with the other parts as well. Let me know!

Would you like me to explain anything in more detail or assist with parts 2-4?

Here are 5 related questions you might find helpful:

1. How do you evaluate functions with fractional bases?
2. What is the effect of negative exponents in rational functions?
3. What are other exponent rules I should know for simplifying expressions?
4. How does rounding to decimal places work in mathematical calculations?
5. How can I graph exponential functions like this one?

Tip: When dealing with negative exponents, always remember that they imply a reciprocal.