The graph you provided consists of three line segments. To express this graph as a piecewise function, we need to identify the equation for each line segment and their respective domains. Let's break down the segments:

1. Horizontal Line Segment:

• This segment is a horizontal line from $(-4, 7)$ to $(1, 7)$.
• The line's equation is simply $y = 7$ because the $y$-value remains constant.
• The domain is $-4 < x \leq 1$, as there is an open circle at $(-4, 7)$ and a closed circle at $(1, 7)$.

2. Vertical Line Segment:

• This is a vertical line from $(1, 2)$ to $(1, 4)$.
• Since it's vertical, it's described as $x = 1$, but we need to express it in piecewise form for $y$.
• The domain here is for a single $x$-value, but the range of $y$-values is $2 < y \leq 4$. This is tricky because vertical lines aren't functions of $x$, but in piecewise form, we'll represent it within the range for $y$.
• Thus, we write $f(1) = y$ for $2 < y \leq 4$, but this can be captured by the piecewise form later.

3. Diagonal Line Segment:

• This line runs from $(2, 4)$ to $(4, -8)$.
• To find the equation, we first calculate the slope $m$: [ m = \frac{y_2 - y_1}{x_