Evaluate f(-8), f(0), f(x) = f(-8)= f(0) = f(7) = and f(7) for the piecewise defined function. -6 √x + 3 if x < 0 1-x if x ≥ 0 Sketch the graph of the function. -2 y 6 4 -2 y 4 -6 -4 y 6 4 2 y 4
Evaluate f(-8), f(0), f(x) = f(-8)= f(0) = f(7) = and f(7) for the piecewise defined function. -6 √x + 3 if x < 0 1-x if x ≥ 0 Sketch the graph of the function. -2 y 6 4 -2 y 4 -6 -4 y 6 4 2 y 4
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Piecewise Defined Functions and Graphical Representation
#### Problem Statement:
Evaluate \( f(-8) \), \( f(0) \), and \( f(7) \) for the piecewise defined function specified below:
\[ f(x) = \begin{cases}
x + 3 & \text{if } x < 0 \\
1 - x & \text{if } x \geq 0
\end{cases} \]
#### Function Values:
- \( f(-8) = \) ________
- \( f(0) = \) ________
- \( f(7) = \) ________
#### Graph of the Function:
Below are graphical representations of the piecewise defined function.
1. **First Graph:**
- \( x \)-axis ranges from \(-6\) to \(6\).
- \( y \)-axis ranges from \(-6\) to \(6\).
- The graph is composed of two line segments:
- For \( x < 0 \), the function \( f(x) = x + 3 \). This segment appears as a line with a positive slope starting from \(-6, -3\) and continuing through the point \(0, 3\) (excluding the point at \(x=0\)).
- For \( x \geq 0 \), the function \( f(x) = 1 - x \). This segment appears as a line with a negative slope starting from the open circle at \(0, 1\) and continuing through points like \(5, -4\) as \( x \) increases.
- There's a solid dot at the point \( (0, 1) \) indicating the function value at \( x = 0 \) within its domain.
2. **Second Graph:**
- Identical to the first graph in layout, scale, and line segments.
3. **Third Graph:**
- Identical to the first graph in layout, scale, and line segments.
4. **Fourth Graph:**
- Identical to the first graph in layout, scale, and line segments.
#### Graphical Explanation:
Each graph shown is the visual representation of the piecewise function \( f(x) \). The graph clearly illustrates the behavior of \( f \) around the critical point \( x = 0 \) where the definition of the function changes.
- **](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd2a881fc-0749-48b7-aba0-5bec7959e8c8%2Fedf862f3-d11e-41d3-981b-dda09bf7817e%2Fv34woqh_processed.png&w=3840&q=75)
Transcribed Image Text:### Piecewise Defined Functions and Graphical Representation
#### Problem Statement:
Evaluate \( f(-8) \), \( f(0) \), and \( f(7) \) for the piecewise defined function specified below:
\[ f(x) = \begin{cases}
x + 3 & \text{if } x < 0 \\
1 - x & \text{if } x \geq 0
\end{cases} \]
#### Function Values:
- \( f(-8) = \) ________
- \( f(0) = \) ________
- \( f(7) = \) ________
#### Graph of the Function:
Below are graphical representations of the piecewise defined function.
1. **First Graph:**
- \( x \)-axis ranges from \(-6\) to \(6\).
- \( y \)-axis ranges from \(-6\) to \(6\).
- The graph is composed of two line segments:
- For \( x < 0 \), the function \( f(x) = x + 3 \). This segment appears as a line with a positive slope starting from \(-6, -3\) and continuing through the point \(0, 3\) (excluding the point at \(x=0\)).
- For \( x \geq 0 \), the function \( f(x) = 1 - x \). This segment appears as a line with a negative slope starting from the open circle at \(0, 1\) and continuing through points like \(5, -4\) as \( x \) increases.
- There's a solid dot at the point \( (0, 1) \) indicating the function value at \( x = 0 \) within its domain.
2. **Second Graph:**
- Identical to the first graph in layout, scale, and line segments.
3. **Third Graph:**
- Identical to the first graph in layout, scale, and line segments.
4. **Fourth Graph:**
- Identical to the first graph in layout, scale, and line segments.
#### Graphical Explanation:
Each graph shown is the visual representation of the piecewise function \( f(x) \). The graph clearly illustrates the behavior of \( f \) around the critical point \( x = 0 \) where the definition of the function changes.
- **
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