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To determine the correct answer, let's analyze each option by evaluating the function \( f(x) = -\sqrt{x + 4} - 3 \) at specific points.

### Step 1: Rewrite the Function
The function is:
\[
f(x) = -\sqrt{x + 4} - 3
\]

### Step 2: Evaluate the Function at Specific Values
1. **\( f(-3) \):**
   \[
   f(-3) = -\sqrt{-3 + 4} - 3 = -\sqrt{1} - 3 = -1 - 3 = -4
   \]

2. **\( f(-4) \):**
   \[
   f(-4) = -\sqrt{-4 + 4} - 3 = -\sqrt{0} - 3 = 0 - 3 = -3
   \]

3. **\( f(0) \):**
   \[
   f(0) = -\sqrt{0 + 4} - 3 = -\sqrt{4} - 3 = -2 - 3 = -5
   \]

4. **\( f(5) \):**
   \[
   f(5) = -\sqrt{5 + 4} - 3 = -\sqrt{9} - 3 = -3 - 3 = -6
   \]

### Step 3: Check Each Statement
- **Option A: \( f(-3) = f(-4) \)**
  \[
  f(-3) = -4 \quad \text{and} \quad f(-4) = -3
  \]
  This is false since \(-4 \neq -3\).

- **Option B: \( f(-3) > f(-4) \)**
  \[
  f(-3) = -4 \quad \text{and} \quad f(-4) = -3
  \]
  This is false since \(-4 < -3\).

- **Option C: \( f(0) > f(-3) \)**
  \[
  f(0) = -5 \quad \text{and} \quad f(-3) = -4
  \]
  This is false since \(-5 < -4\).

- **Option D: \( f(0) > f(5) \)**
  \[
  f(0) = -5 \quad \text{and} \quad f(5) = -6
  \]
  This is true since \(-5 > -6\).

### Conclusion
The correct answer is:
**D. \( f(0) > f(5) \)**

Would you like further explanation or details on any of these calculations?

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### Follow-up Questions:
1. How do we determine if a function is increasing or decreasing over an interval?
2. What is the effect of negative square roots on function values?
3. How would the answer change if the function had a positive square root term?
4. Why does the value of \( f(x) \) decrease as \( x \) increases in this function?
5. Can we use derivatives to analyze the behavior of this function?

### Tip:
When working with functions involving square roots, check the domain to ensure values under the square root are non-negative.

Given the function f(x) = -√(x + 4) - 3, which statement is true? 
A. f(-3) = f(-4) 
B. f(-3) > f(-4) 
C. f(0) > f(-3) 
D. f(0) > f(5)

Learn how to determine the true statement about the function f(x) = -√(x + 4) - 3 by evaluating it at various points. Understand concepts such as function evaluation, square roots, and inequalities. Suitable for Grades 9-11.

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