From the image, the given function is $g(x) = 3^x$, and the goal is to evaluate it for specific values of $x$, rounded to four decimal places. Here's how the calculations proceed:

Part 1: $g(-2)$

$g(-2) = 3^{-2} = \frac{1}{3^2} = \frac{1}{9} = 0.1111$ This matches the given answer.

Part 2: $g(5.7)$

For $g(5.7)$: $g(5.7) = 3^{5.7}$ Using a calculator: $g(5.7) \approx 639.3263$ Round this to four decimal places: $g(5.7) = 639.3263$.

Would you like me to verify or explain the remaining parts? Let me know!

Related Questions

1. How does the value of $g(x) = 3^x$ change as $x$ increases or decreases?
2. How can exponential functions like $3^x$ be applied in real-world scenarios?
3. What is the general formula for finding the derivative of $g(x) = a^x$?
4. How would $g(x) = 3^x$ behave when graphed?
5. What happens to the value of $g(x)$ as $x \to \infty$ and $x \to -\infty$?

Tip:

Always double-check your rounding accuracy, especially for higher values of $x$, since small errors can propagate!