Starting with the graph of f(x) = 2, write the equation of the graph that results from (a) shifting f(x) 1 units upward. y = (b) shifting f(x) 1 units to the right. y = (c) reflecting f(x) about the x-axis and the y-axis. y =
Starting with the graph of f(x) = 2, write the equation of the graph that results from (a) shifting f(x) 1 units upward. y = (b) shifting f(x) 1 units to the right. y = (c) reflecting f(x) about the x-axis and the y-axis. y =
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
![**Transformations of Exponential Functions**
Starting with the graph of \( f(x) = 2^x \), write the equation of the graph that results from:
1. **Shifting \( f(x) \) 1 unit upward.**
- \( y = \) [Input the transformed equation here]
2. **Shifting \( f(x) \) 1 unit to the right.**
- \( y = \) [Input the transformed equation here]
3. **Reflecting \( f(x) \) about the x-axis and the y-axis.**
- \( y = \) [Input the transformed equation here]
For shifting 1 unit upward, you need to add 1 to the function: \( y = 2^x + 1 \).
For shifting 1 unit to the right, you replace \( x \) with \( x-1 \): \( y = 2^{(x-1)} \).
For reflecting about both the x-axis and the y-axis, you negate both \( x \) and the entire function: \( y = -2^{-x} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F11f50382-dc41-434c-a8e4-3cb9cbf912c9%2F710a5529-529f-49b0-be77-d0c813d3c182%2Fnw9g0of_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Transformations of Exponential Functions**
Starting with the graph of \( f(x) = 2^x \), write the equation of the graph that results from:
1. **Shifting \( f(x) \) 1 unit upward.**
- \( y = \) [Input the transformed equation here]
2. **Shifting \( f(x) \) 1 unit to the right.**
- \( y = \) [Input the transformed equation here]
3. **Reflecting \( f(x) \) about the x-axis and the y-axis.**
- \( y = \) [Input the transformed equation here]
For shifting 1 unit upward, you need to add 1 to the function: \( y = 2^x + 1 \).
For shifting 1 unit to the right, you replace \( x \) with \( x-1 \): \( y = 2^{(x-1)} \).
For reflecting about both the x-axis and the y-axis, you negate both \( x \) and the entire function: \( y = -2^{-x} \).
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