https://file.aiquickdraw.com/mathbot/file/172675369678988wpsvoc.jpg

The given piecewise function is:

\[
g(x) = \begin{cases} 
-3x & \text{for } 0 \leq x < 2 \\
12 & \text{for } x \geq 2
\end{cases}
\]

Let's evaluate the function at the given points.

1. **\( g(0) \):**
   Since \( 0 \leq x < 2 \), use the first case \( g(x) = -3x \).
   \[
   g(0) = -3(0) = 0
   \]

2. **\( g(2) \):**
   Since \( x = 2 \) falls in the second case \( x \geq 2 \), use the second case \( g(x) = 12 \).
   \[
   g(2) = 12
   \]

3. **\( g(4) \):**
   Since \( x = 4 \geq 2 \), it falls in the second case again.
   \[
   g(4) = 12
   \]

### Final Results:
- \( g(0) = 0 \)
- \( g(2) = 12 \)
- \( g(4) = 12 \)

Would you like further explanation or have any other questions?

Here are 5 related questions to think about:
1. What would \( g(1) \) be for this function?
2. How does the function behave for negative values of \( x \)?
3. What would happen if the function had more pieces for different ranges of \( x \)?
4. Can you graph the piecewise function? What would the graph look like?
5. How would the function change if the second piece was quadratic instead of constant?

**Tip:** When working with piecewise functions, always check which interval the input falls into before applying the formula.

Determine the value of each piecewise-defined function, g(x), where g(x) = -3x for 0 ≤ x < 2 and g(x) = 12 for x ≥ 2. What are g(0), g(2), and g(4)?

Learn how to evaluate a piecewise-defined function where g(x) is defined by two parts: g(x) = -3x for 0 ≤ x < 2, and g(x) = 12 for x ≥ 2. Find the values of g(0), g(2), and g(4).

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