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To solve the expression \( 3f(4) + f(0) - \frac{1}{2} f(-3) \), we need to first determine the values of \( f(4) \), \( f(0) \), and \( f(-3) \) from the graph provided.

### Step 1: Extract Values from the Graph
- **\( f(4) \):** Find the y-coordinate where \( x = 4 \).
- **\( f(0) \):** Find the y-coordinate where \( x = 0 \).
- **\( f(-3) \):** Find the y-coordinate where \( x = -3 \).

### Step 2: Substitute Values into the Expression
Once we have these values, we will substitute them into the expression \( 3f(4) + f(0) - \frac{1}{2} f(-3) \) to find the final result.

Let's examine the graph closely:

- **\( f(4) \):** The graph shows that when \( x = 4 \), \( y = 2 \). So, \( f(4) = 2 \).
- **\( f(0) \):** The graph shows that when \( x = 0 \), \( y = 3 \). So, \( f(0) = 3 \).
- **\( f(-3) \):** The graph shows that when \( x = -3 \), \( y = -1 \). So, \( f(-3) = -1 \).

### Step 3: Calculate the Expression
Now, substitute these values into the expression:

\[
3f(4) + f(0) - \frac{1}{2} f(-3) = 3(2) + 3 - \frac{1}{2}(-1)
\]

Simplify it:

\[
= 6 + 3 + \frac{1}{2} = 9 + 0.5 = 9.5
\]

### Final Answer:
The value of \( 3f(4) + f(0) - \frac{1}{2} f(-3) \) is \( \boxed{9.5} \).

Would you like further details or have any other questions?

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**Related Questions:**
1. What would \( 2f(-2) + f(1) - f(5) \) equal given the same graph?
2. How does the slope of the line between \( f(-5) \) and \( f(-2) \) compare with the slope between \( f(0) \) and \( f(3) \)?
3. What is the maximum value of \( f(x) \) on the interval \([-5, 5]\)?
4. Can you derive the equation of the line segment connecting \( (-5, -2) \) and \( (0, 3) \)?
5. What is the domain and range of the function \( f(x) \) based on the graph?

**Tip:** Always check the coordinates on the graph carefully to ensure accuracy when reading values directly from it.

Learn how to solve the expression 3f(4) + f(0) - 1/2 f(-3) by interpreting values from a graph. This problem is suitable for Grades 9-11 and covers key concepts like function evaluation and graph interpretation.

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