https://file.aiquickdraw.com/mathbot/file/1726848224935o80vbsfz.jpg

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_

Express the function graphed on the axes below as a piecewise function.

Learn how to express a graphed function as a piecewise function. This problem involves identifying line segments, calculating slopes, and defining each segment within its respective domain. Suitable for high school students studying algebra and functions.

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