1. The problem asks to write the equations of a house-like graph composed of lines and curves using square roots, absolute values, and quadratic forms, with vertical and horizontal boundaries. 2. The given inequalities and equations describe segments of the graph: - $y = \{ x < 9 \}$ means the domain is restricted to $x < 9$. - $y = - \{ x < 6 \} + 1$ suggests a line or curve with domain $x < 6$ shifted up by 1. - $y = - \{ x < 10 \} + 13$ suggests a line or curve with domain $x < 10$ shifted up by 13. - $y = -(x - 2) \{ 4.6 < x < 7.4 \}$ is a linear segment between $x=4.6$ and $x=7.4$. - $y = -\sqrt{x} \{ 5 < x < 8 \}$ is a curve defined by the negative square root of $x$ between $x=5$ and $x=8$. 3. To write explicit equations, we interpret the notation as piecewise functions with domain restrictions: $$ \begin{cases} \text{Segment 1: } y = \text{some function}, & x < 9 \\ \text{Segment 2: } y = -f(x) + 1, & x < 6 \\ \text{Segment 3: } y = -g(x) + 13, & x < 10 \\ \text{Segment 4: } y = -(x - 2), & 4.6 < x < 7.4 \\ \text{Segment 5: } y = -\sqrt{x}, & 5 < x < 8 \end{cases} $$ 4. Since the problem states 7 equations were used, and the graph is house-like with a peaked roof and rectangular walls, the likely equations are: - Left vertical wall: $x = a$ (vertical line) - Right vertical wall: $x = b$ (vertical line) - Base horizontal line: $y = c$ (horizontal line) - Roof peak line segments: linear equations with domain restrictions - Curved segments near base: square root or absolute value functions with domain restrictions 5. Example explicit equations matching the description: - Left wall: $x = 4.6$ - Right wall: $x = 9$ - Base: $y = 0$ - Roof left slope: $y = -(x - 2)$ for $4.6 < x < 7.4$ - Roof right slope: $y = -(x - 10) + 13$ for $7.4 < x < 9$ - Curved base left: $y = -\sqrt{x}$ for $5 < x < 8$ - Curved base right: $y = -|x - 7| + 1$ for $x < 6$ 6. These equations combine to form the house shape with vertical walls, a peaked roof, and curved base segments. Final answer: $$ \begin{cases} x = 4.6 \\ x = 9 \\ y = 0 \\ y = -(x - 2), & 4.6 < x < 7.4 \\ y = -(x - 10) + 13, & 7.4 < x < 9 \\ y = -\sqrt{x}, & 5 < x < 8 \\ y = -|x - 7| + 1, & x < 6 \end{cases} $$