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The given function is a piecewise function:

\[
f(x) = 
\begin{cases} 
-3 - 2x, & x \geq -3 \\
-x^2 + 7, & x < -3
\end{cases}
\]

We are asked to find \( f(-3) + f(-2) \).

### Step 1: Find \( f(-3) \)

Since \( -3 \geq -3 \), we use the first piece of the function:

\[
f(-3) = -3 - 2(-3) = -3 + 6 = 3
\]

### Step 2: Find \( f(-2) \)

Since \( -2 \geq -3 \), we again use the first piece of the function:

\[
f(-2) = -3 - 2(-2) = -3 + 4 = 1
\]

### Step 3: Calculate \( f(-3) + f(-2) \)

\[
f(-3) + f(-2) = 3 + 1 = 4
\]

### Final Answer:

The value of \( f(-3) + f(-2) \) is \( 4 \).

---

Would you like more details or explanations on any of the steps? 

Here are five related questions to deepen your understanding:
1. What is a piecewise function and how is it applied in general?
2. How would you find the value of \( f(x) \) for \( x = -4 \)?
3. What happens if we change the boundary condition \( x \geq -3 \) to \( x > -3 \)?
4. How does the quadratic form of the second piece influence the function's graph?
5. How would you plot the given function on a graph?

**Tip:** Always check the domain of each piece in a piecewise function before calculating values.

What is the value of f(-3) + f(-2) for the given piecewise function?

Solve the piecewise function f(x) = -3 - 2x for x >= -3 and f(x) = -x^2 + 7 for x < -3 to find the value of f(-3) + f(-2). Learn how to evaluate such functions step by step, covering core algebra concepts.

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