1. **Problem statement:** Write equations for the modular functions $f(x)$, $g(x)$, and $h(x)$ given their graphs with vertices at $(-4,0)$, $(0,0)$, and $(3,0)$ respectively. 2. **Recall the form of modular functions:** A modular function with vertex at $(c,0)$ can be written as $$f(x) = |x - c|$$ This is because the absolute value function shifts horizontally to the vertex $c$. 3. **Apply the formula to each function:** - For $f(x)$ with vertex at $(-4,0)$: $$f(x) = |x - (-4)| = |x + 4|$$ - For $g(x)$ with vertex at $(0,0)$: $$g(x) = |x - 0| = |x|$$ - For $h(x)$ with vertex at $(3,0)$: $$h(x) = |x - 3|$$ 4. **Explanation:** Each function is a V-shaped graph centered at its vertex. The absolute value expression $|x - c|$ shifts the graph horizontally so that the vertex is at $x = c$. The $y$-value is always non-negative, reflecting the V shape. **Final answers:** $$f(x) = |x + 4|$$ $$g(x) = |x|$$ $$h(x) = |x - 3|$$