Describe g(x) in terms of f(x) if the graph of g is obtained by vertically stretching ƒ by a factor of 2, then shifting the graph of f to the right 2 units, then shifting upward 8 units. g(x) = Af(x + B) + C where А — В =
Describe g(x) in terms of f(x) if the graph of g is obtained by vertically stretching ƒ by a factor of 2, then shifting the graph of f to the right 2 units, then shifting upward 8 units. g(x) = Af(x + B) + C where А — В =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![**Question: Transformation of Functions**
Describe \( g(x) \) in terms of \( f(x) \) if the graph of \( g \) is obtained by vertically stretching \( f \) by a factor of 2, then shifting the graph of \( f \) to the right 2 units, then shifting upward 8 units.
\[ g(x) = Af(x + B) + C \text{ where} \]
\[ A = \]
\[ B = \]
\[ C = \]
**Explanation:**
1. **Vertical Stretch**: This affects the coefficient \( A \). A vertical stretch by a factor of 2 means \( A = 2 \).
2. **Horizontal Shift (Right 2 Units)**: This affects the parameter \( B \). Shifting to the right by 2 units means \( B = -2 \).
3. **Vertical Shift (Upward 8 Units)**: This parameter is \( C \). Shifting upward by 8 units means \( C = 8 \).
Therefore, the values are:
\[ A = 2 \]
\[ B = -2 \]
\[ C = 8 \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc4e7be12-e868-44b9-86d4-0a000fb9596b%2F8b7085cf-b1ee-4106-971a-6fefb9dce41e%2F6xit3k_processed.png&w=3840&q=75)
Transcribed Image Text:**Question: Transformation of Functions**
Describe \( g(x) \) in terms of \( f(x) \) if the graph of \( g \) is obtained by vertically stretching \( f \) by a factor of 2, then shifting the graph of \( f \) to the right 2 units, then shifting upward 8 units.
\[ g(x) = Af(x + B) + C \text{ where} \]
\[ A = \]
\[ B = \]
\[ C = \]
**Explanation:**
1. **Vertical Stretch**: This affects the coefficient \( A \). A vertical stretch by a factor of 2 means \( A = 2 \).
2. **Horizontal Shift (Right 2 Units)**: This affects the parameter \( B \). Shifting to the right by 2 units means \( B = -2 \).
3. **Vertical Shift (Upward 8 Units)**: This parameter is \( C \). Shifting upward by 8 units means \( C = 8 \).
Therefore, the values are:
\[ A = 2 \]
\[ B = -2 \]
\[ C = 8 \]
Expert Solution
Step 1
Given that the graph of g is obtained by vertically stretching f by a factor of 2
I. e. 1st step is g(x)=2f(x)
Step by step
Solved in 3 steps
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