1. The problem is to find the domain of the function represented by the blue line segment on the coordinate plane. 2. The graph shows a line segment starting at the point $(-4,-4)$ and ending at the point $(5,1)$. 3. Since the line segment includes both endpoints (solid dots), the domain includes all $x$ values from $-4$ to $5$ inclusive. 4. Therefore, the domain is the closed interval $$[-4,5].$$ This means the function is defined for all $x$ such that $-4 \leq x \leq 5$.