1. The problem asks to find the value of the function $f(x)$ at $x = -4$ for a piecewise linear function described by a triangular shape. 2. The function increases linearly from $y=0$ at $x=-10$ to $y=5$ at $x=-5$, then decreases linearly from $y=5$ at $x=-5$ to $y=-10$ at $x=10$. 3. Since $-4$ is between $-5$ and $10$, we use the second linear segment from $(-5,5)$ to $(10,-10)$. 4. The slope $m$ of this segment is calculated by $$m = \frac{-10 - 5}{10 - (-5)} = \frac{-15}{15} = -1.$$ 5. The equation of the line segment is $$y - 5 = -1(x + 5)$$ which simplifies to $$y = -x - 5 + 5 = -x.$$ 6. Substitute $x = -4$ into the equation: $$f(-4) = -(-4) = 4.$$ 7. Therefore, the value of $f(-4)$ is 4.