if x < -2 Sketch a graph of f(x) = x-1 if -2 1 Note: Be sure to include closed or open dots, but only at breaks in the graph. -5 -4 -3 -2 -1 5+ 4 3 2 1 -1 -2- -3 -N 2 3 4

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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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### Piecewise Function Graphing Tutorial

#### Problem Statement

**Sketch a graph of \( f(x) \):**

\[ 
f(x) = 
\begin{cases} 
-3 & \text{if } x \leq -2 \\ 
x - 1 & \text{if } -2 < x \leq 1 \\ 
-3 & \text{if } x > 1 
\end{cases} 
\]

**Note**: Be sure to include closed or open dots, but only at breaks in the graph.

#### Graphing Instructions

1. **Graph the first piece**:

   For \( x \leq -2 \), the function \( f(x) = -3 \).

   - Draw a horizontal line at \( y = -3 \) for \( x \leq -2 \).
   - Place a closed dot at \( (-2, -3) \).

2. **Graph the second piece**:

   For \( -2 < x \leq 1 \), the function \( f(x) = x - 1 \).

   - This is a linear function. Plot the line segment starting just after \( x = -2 \) and ending at \( x = 1 \).
   - Place an open dot at \( (-2, -3) \).
   - Since \( f(x) = x - 1 \), at \( x = -2 \), \( f(x) = -3 \),
   - At \( x = 1 \), \( f(x) = 0 \), place a closed dot at \( (1, 0) \).

3. **Graph the third piece**:

   For \( x > 1 \), the function \( f(x) = -3 \).

   - Draw a horizontal line at \( y = -3 \) for \( x > 1 \).
   - Place an open dot at \( (1, -3) \).

#### Explanation of the Graph Layout

- **Axes**: The x-axis ranges from -5 to 5 and the y-axis ranges from -5 to 5.
- **Detailed Steps**:
  - Plot horizontal line at \( y = -3 \) from \( x = -5 \) to \( x = -2 \) with a closed dot at \( (-2, -3) \).
  - Plot the linear segment from just after \(
Transcribed Image Text:### Piecewise Function Graphing Tutorial #### Problem Statement **Sketch a graph of \( f(x) \):** \[ f(x) = \begin{cases} -3 & \text{if } x \leq -2 \\ x - 1 & \text{if } -2 < x \leq 1 \\ -3 & \text{if } x > 1 \end{cases} \] **Note**: Be sure to include closed or open dots, but only at breaks in the graph. #### Graphing Instructions 1. **Graph the first piece**: For \( x \leq -2 \), the function \( f(x) = -3 \). - Draw a horizontal line at \( y = -3 \) for \( x \leq -2 \). - Place a closed dot at \( (-2, -3) \). 2. **Graph the second piece**: For \( -2 < x \leq 1 \), the function \( f(x) = x - 1 \). - This is a linear function. Plot the line segment starting just after \( x = -2 \) and ending at \( x = 1 \). - Place an open dot at \( (-2, -3) \). - Since \( f(x) = x - 1 \), at \( x = -2 \), \( f(x) = -3 \), - At \( x = 1 \), \( f(x) = 0 \), place a closed dot at \( (1, 0) \). 3. **Graph the third piece**: For \( x > 1 \), the function \( f(x) = -3 \). - Draw a horizontal line at \( y = -3 \) for \( x > 1 \). - Place an open dot at \( (1, -3) \). #### Explanation of the Graph Layout - **Axes**: The x-axis ranges from -5 to 5 and the y-axis ranges from -5 to 5. - **Detailed Steps**: - Plot horizontal line at \( y = -3 \) from \( x = -5 \) to \( x = -2 \) with a closed dot at \( (-2, -3) \). - Plot the linear segment from just after \(
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