We are given the function $f(x) = -\frac{1}{2} |x - 2| + 4$. To find $f(3)$, we substitute $x = 3$ into the equation:

$f(3) = -\frac{1}{2} |3 - 2| + 4$

First, calculate $|3 - 2|$:

$|3 - 2| = 1$

Now substitute this value back into the equation:

$f(3) = -\frac{1}{2} \times 1 + 4$

Simplify:

$f(3) = -\frac{1}{2} + 4 = \frac{7}{2}$

Thus, $f(3) = \frac{7}{2}$ or 3.5.

Do you want more details on how absolute values work in functions?

Here are 5 relative questions:

1. How does the absolute value affect the graph of a function?
2. What happens to the function as $x$ increases or decreases in $f(x) = -\frac{1}{2} |x-2| + 4$?
3. Can you describe the vertex of the function $f(x) = -\frac{1}{2} |x - 2| + 4$?
4. How would $f(x)$ change if the coefficient of the absolute value term were positive?
5. What is the domain and range of this function?

Tip: For absolute value functions, the graph often forms a "V" shape, and the vertex represents the point where the expression inside the absolute value equals zero.