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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![**Graphing Function Transformations**
**Objective:**
Use the graph of \( y = f(x) \) shown to the right to graph the following function \( g \).
**Function to Graph:**
\[ g(x) = -f \left( -\frac{1}{2}x \right) - 3 \]
**Given Graph:**
- The provided graph is of \( y = f(x) \).
- Key points on the graph: (-3,1), (0,1), (3,1).
A detailed look at the given graph:
- The x-axis ranges from -8 to 8.
- The y-axis ranges from 0 to 9.
- The graph depicts a horizontal line \(y = 1\).
**Task:**
Choose the graph that correctly represents the transformed function \( g(x) \).
**Transformation Steps:**
1. **Horizontal Stretch and Reflection:**
- Inside the function \(f\), the term \(-\frac{1}{2}x\) suggests a horizontal stretch by a factor of 2 (since \(\frac{1}{2}\)), and reflects across the y-axis (because of the negative sign).
2. **Vertical Reflection:**
- The negative sign outside \(f\) indicates a reflection across the x-axis.
3. **Vertical Translation:**
- The term \(-3\) indicates that the function is shifted downward by 3 units.
**Choices:**
- **Choice A**
- This graph shows a horizontal line segment at \( y = -3 \) from \( x = -6 \) to \( x = 6 \).
- **Choice B**
- This graph shows a horizontal line segment at \( y = -4 \).
- **Choice C**
- This graph shows a horizontal line segment at \( y = -2 \).
- **Choice D**
- This graph shows a horizontal line segment at \( y = 3 \).
Evaluate the transformations and select the correct graph.
**Correct Answer:**
Choose the graph that corresponds to the transformed function \( g(x) = -f \left( -\frac{1}{2}x \right) - 3 \).
(Insert answer key based on correct transformation).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F27eac774-32b6-4ca9-bd68-32e8b5bccb2f%2F0f744c87-7e8f-49a3-a9ba-4fc51b8ffc6c%2Fdmg6qkq_processed.png&w=3840&q=75)
Transcribed Image Text:**Graphing Function Transformations**
**Objective:**
Use the graph of \( y = f(x) \) shown to the right to graph the following function \( g \).
**Function to Graph:**
\[ g(x) = -f \left( -\frac{1}{2}x \right) - 3 \]
**Given Graph:**
- The provided graph is of \( y = f(x) \).
- Key points on the graph: (-3,1), (0,1), (3,1).
A detailed look at the given graph:
- The x-axis ranges from -8 to 8.
- The y-axis ranges from 0 to 9.
- The graph depicts a horizontal line \(y = 1\).
**Task:**
Choose the graph that correctly represents the transformed function \( g(x) \).
**Transformation Steps:**
1. **Horizontal Stretch and Reflection:**
- Inside the function \(f\), the term \(-\frac{1}{2}x\) suggests a horizontal stretch by a factor of 2 (since \(\frac{1}{2}\)), and reflects across the y-axis (because of the negative sign).
2. **Vertical Reflection:**
- The negative sign outside \(f\) indicates a reflection across the x-axis.
3. **Vertical Translation:**
- The term \(-3\) indicates that the function is shifted downward by 3 units.
**Choices:**
- **Choice A**
- This graph shows a horizontal line segment at \( y = -3 \) from \( x = -6 \) to \( x = 6 \).
- **Choice B**
- This graph shows a horizontal line segment at \( y = -4 \).
- **Choice C**
- This graph shows a horizontal line segment at \( y = -2 \).
- **Choice D**
- This graph shows a horizontal line segment at \( y = 3 \).
Evaluate the transformations and select the correct graph.
**Correct Answer:**
Choose the graph that corresponds to the transformed function \( g(x) = -f \left( -\frac{1}{2}x \right) - 3 \).
(Insert answer key based on correct transformation).
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