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
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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**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:

\[ A = 2 \]
\[ B = -2 \]
\[ C = 8 \]
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)

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