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The problem asks to find the values of the piecewise function \( g(x) \) at specific points. The function is given as:

\[
g(x) =
\begin{cases}
x + 9, & \text{for } x \leq 2 \\
6 - x, & \text{for } x > 2
\end{cases}
\]

You need to calculate \( g(-4) \), \( g(2) \), and \( g(9) \).

### 1. \( g(-4) \):
Since \( -4 \leq 2 \), use the first part of the piecewise function \( g(x) = x + 9 \):
\[
g(-4) = -4 + 9 = 5
\]

### 2. \( g(2) \):
Since \( 2 \leq 2 \), use the first part of the piecewise function \( g(x) = x + 9 \):
\[
g(2) = 2 + 9 = 11
\]

### 3. \( g(9) \):
Since \( 9 > 2 \), use the second part of the piecewise function \( g(x) = 6 - x \):
\[
g(9) = 6 - 9 = -3
\]

### Final Answers:
- \( g(-4) = 5 \)
- \( g(2) = 11 \)
- \( g(9) = -3 \)

Would you like further clarification on any part of the solution?

Here are five related questions to practice:
1. What is the value of \( g(0) \) for the same piecewise function?
2. How would you find \( g(3) \)?
3. Can you graph the piecewise function \( g(x) \)?
4. What happens to \( g(x) \) as \( x \) approaches infinity?
5. How would you modify the function if the condition for the second part was \( x \geq 3 \) instead of \( x > 2 \)?

**Tip:** Always check which condition of the piecewise function applies before evaluating it at a specific value of \( x \).

For the piecewise function, find the values g(-4), g(2), and g(9). The function is given by: g(x) = { x + 9, for x ≤ 2; 6 - x, for x > 2 }

Learn how to evaluate a piecewise function at specific values. This problem covers the process of determining g(-4), g(2), and g(9) using two distinct conditions for x. Suitable for students in Grades 7-9.

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