https://file.aiquickdraw.com/mathbot/file/1725983294144682ga1ru.jpg

The piecewise function is given as:

\[
f(x) = 
\begin{cases} 
-8 & \text{if } x \leq -5 \\
0 & \text{if } -5 < x < 5 \\
5 & \text{if } x \geq 5 
\end{cases}
\]

You need to evaluate \( f(x) \) for \( x = -6 \) and \( x = 5 \).

### For \( x = -6 \):
Since \( x = -6 \) is less than or equal to \(-5\), we use the first condition of the function:

\[
f(-6) = -8
\]

### For \( x = 5 \):
Since \( x = 5 \) is greater than or equal to 5, we use the third condition of the function:

\[
f(5) = 5
\]

Thus, \( f(-6) = -8 \) and \( f(5) = 5 \).

### Correct Answer:
The correct option is:
\[
\boxed{f(-6) = -8 \quad \text{and} \quad f(5) = 5}
\]

Do you want further details or have any questions?

Here are 5 related questions to expand on this:

1. How would the function behave for values of \( x = 0 \)?
2. Can you describe the overall shape of this piecewise function graphically?
3. What is the domain and range of this function?
4. How would you evaluate \( f(x) \) for \( x = -5 \)?
5. What is the limit of \( f(x) \) as \( x \) approaches 5 from the left and right?

**Tip:** When evaluating piecewise functions, always check which condition of the function applies to your input.

Evaluate the function for the given values of x. f(x) is a piecewise function defined as: f(x) = -8 if x ≤ -5, f(x) = 0 if -5 < x < 5, and f(x) = 5 if x ≥ 5. Find f(-6) and f(5).

Learn how to evaluate a piecewise function for the given values of x. The function has different rules for x less than, between, and greater than 5. This problem involves evaluating f(-6) and f(5), ideal for students in Grades 9-10.

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