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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Question
![Use the graph of \( y = f(x) \) shown to the right to graph the following function \( g \):
\[ g(x) = -\frac{1}{2} f(x+4) - 2 \]
Choose the correct graph below:
- Option A
- Option B
- Option C
- Option D
**Graph Description:**
1. **Reference Graph (Top Right):**
- This graph represents \( y = f(x) \). It is labeled with the axes \( x \) and \( y \), and shows the curve or line representing the function \( f(x) \).
2. **Options A, B, C, and D (Bottom):**
- Each option shows a graph on a grid with axes labeled \( x \) and \( y \).
- The graphs differ in the position and orientation of the function curve, displaying possible results of the transformation applied to \( f(x) \) as given by \( g(x) = -\frac{1}{2} f(x+4) - 2 \).
**Explanation of Transformation:**
The transformation of the function \( f(x) \) to \( g(x) \) involves:
- **Horizontal Shift:** \( f(x+4) \) indicates a shift to the left by 4 units.
- **Vertical Stretch and Reflection:** The multiplication by \(-\frac{1}{2}\) reflects the graph across the x-axis and scales it vertically by a factor of \(\frac{1}{2}\).
- **Vertical Shift:** The subtraction of 2 shifts the graph downwards by 2 units.
Selecting the correct graph involves identifying these transformations in the options provided.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fee5144b1-2276-4010-857d-2387de3c8638%2Fb809e454-3f6d-4c01-8669-232871654644%2Fandpfv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Use the graph of \( y = f(x) \) shown to the right to graph the following function \( g \):
\[ g(x) = -\frac{1}{2} f(x+4) - 2 \]
Choose the correct graph below:
- Option A
- Option B
- Option C
- Option D
**Graph Description:**
1. **Reference Graph (Top Right):**
- This graph represents \( y = f(x) \). It is labeled with the axes \( x \) and \( y \), and shows the curve or line representing the function \( f(x) \).
2. **Options A, B, C, and D (Bottom):**
- Each option shows a graph on a grid with axes labeled \( x \) and \( y \).
- The graphs differ in the position and orientation of the function curve, displaying possible results of the transformation applied to \( f(x) \) as given by \( g(x) = -\frac{1}{2} f(x+4) - 2 \).
**Explanation of Transformation:**
The transformation of the function \( f(x) \) to \( g(x) \) involves:
- **Horizontal Shift:** \( f(x+4) \) indicates a shift to the left by 4 units.
- **Vertical Stretch and Reflection:** The multiplication by \(-\frac{1}{2}\) reflects the graph across the x-axis and scales it vertically by a factor of \(\frac{1}{2}\).
- **Vertical Shift:** The subtraction of 2 shifts the graph downwards by 2 units.
Selecting the correct graph involves identifying these transformations in the options provided.
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