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Evaluate f(-3) in the piecewise function below.

To evaluate \( f(-3) \) in the given piecewise function, we need to determine which piece applies for \( x = -3 \).

The piecewise function is:

\[
f(x) = 
\begin{cases} 
x - 6 & \text{for } x \leq -3 \\
5 & \text{for } -3 < x \leq 5 \\
-x + 8 & \text{for } x \geq 6
\end{cases}
\]

Since \( -3 \leq -3 \), the first condition \( x - 6 \) applies when \( x \leq -3 \).

Now, substituting \( x = -3 \) into the first piece:

\[
f(-3) = -3 - 6 = -9
\]

Thus, \( f(-3) = -9 \).

Would you like further details, or do you have any questions? Here are 5 related questions for practice:

1. What is \( f(-4) \)?
2. What is \( f(0) \)?
3. What is the value of \( f(6) \)?
4. How would you graph the piecewise function?
5. What is the domain and range of this function?

**Tip:** Always check which condition applies before evaluating a piecewise function.

In this example, learn how to evaluate f(-3) in a piecewise function with different conditions based on the value of x. The function consists of three pieces: f(x) = x - 6, f(x) = 5, and f(x) = -x + 8. The problem covers concepts from algebra and is suitable for high school students in grades 9-12.

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