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The given function is defined as a piecewise function:

\[
f(x) = 
\begin{cases} 
-x^2 - 4x & \text{if } x \leq 0 \\
x & \text{if } x > 0 
\end{cases}
\]

We are asked to evaluate \( f(-3) \). Since \( -3 \leq 0 \), we will use the first piece of the function:

\[
f(x) = -x^2 - 4x \quad \text{for } x \leq 0
\]

Substitute \( x = -3 \):

\[
f(-3) = -(-3)^2 - 4(-3)
\]

\[
= -(9) + 12 = -9 + 12 = 3
\]

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

The correct answer is **3**.

Would you like further details or have any questions?

Here are 5 related questions for further practice:
1. How would you evaluate \( f(2) \) for the given function?
2. What is the value of \( f(0) \) in this piecewise function?
3. How does the behavior of the function differ for \( x \leq 0 \) and \( x > 0 \)?
4. What are the key characteristics of a piecewise function?
5. Can you find the domain and range of this function?

**Tip:** Always pay close attention to which piece of a piecewise function applies based on the input value.

Evaluate f(-3). The function f(x) is defined as a piecewise function: f(x) = { -x^2 - 4x, if x <= 0; x, if x > 0 }

Learn how to evaluate the piecewise function f(x) where f(x) = -x^2 - 4x for x <= 0 and f(x) = x for x > 0. This problem involves substitution and solving quadratic expressions, suitable for Grades 9-12.

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