https://file.aiquickdraw.com/mathbot/file/1726089600561goiaqzwg.jpg

The piecewise function given in the image is:

\[
h(x) =
\begin{cases}
-3x, & \text{if } x < 2 \\
4x + 1, & \text{if } x \geq 2
\end{cases}
\]

We need to find the value of \( 3h(-2) \).

### Step 1: Find \( h(-2) \)
Since \( -2 < 2 \), we use the first part of the piecewise function, \( h(x) = -3x \).

\[
h(-2) = -3(-2) = 6
\]

### Step 2: Multiply by 3 to get \( 3h(-2) \)
\[
3h(-2) = 3 \times 6 = 18
\]

Thus, the value of \( 3h(-2) \) is \( \boxed{18} \), which matches the selected answer.

Would you like any further explanation or details?

Here are five related questions for further practice:
1. What is the value of \( h(2) \)?
2. Find the value of \( 2h(1) \).
3. What is the domain of the function \( h(x) \)?
4. Evaluate \( h(0) \) and \( h(3) \).
5. For what values of \( x \) does \( h(x) = 1 \)?

**Tip:** Always carefully check which part of a piecewise function applies to the given input value!

Given the piecewise function h(x) = { -3x, x < 2; 4x + 1, x >= 2 }, find the value of 3h(-2).

Learn how to evaluate the value of 3h(-2) for the piecewise function h(x). This problem involves key algebraic concepts and helps reinforce understanding of piecewise functions. Suitable for students in Grades 9-10.

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