https://file.aiquickdraw.com/mathbot/file/1726616126975rge7o07p.jpg

We are given the piecewise function:

\[
g(x) =
\begin{cases} 
x + 6 & \text{for } x \leq 4 \\
8 - x & \text{for } x > 4 
\end{cases}
\]

We need to evaluate \( g(-6) \), \( g(4) \), and \( g(8) \).

### Step-by-Step Calculations:

1. **For \( g(-6) \)**:
   Since \( -6 \leq 4 \), we use the first part of the piecewise function:
   \[
   g(-6) = -6 + 6 = 0
   \]

2. **For \( g(4) \)**:
   Since \( 4 \leq 4 \), we also use the first part of the function:
   \[
   g(4) = 4 + 6 = 10
   \]

3. **For \( g(8) \)**:
   Since \( 8 > 4 \), we use the second part of the function:
   \[
   g(8) = 8 - 8 = 0
   \]

### Final Values:
\[
g(-6) = 0, \quad g(4) = 10, \quad g(8) = 0
\]

Let me know if you'd like further details, and here are some related questions to explore:

1. What is \( g(0) \)?
2. What is the domain of the function \( g(x) \)?
3. How does the function behave at the boundary \( x = 4 \)?
4. What is the range of \( g(x) \)?
5. How would the function change if the condition for \( x > 4 \) was modified?

**Tip**: Always check the condition of a piecewise function to determine which part of the function to use for evaluation.

For the piecewise function, find the values g(-6), g(4), and g(8). g(x) = {x + 6 for x ≤ 4, 8 - x for x > 4}

Discover how to evaluate the piecewise function g(x) at specific points: g(-6), g(4), and g(8), with clear explanations of which part of the function to use based on the value of x. Suitable for high school students learning about piecewise functions and function evaluation.

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