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Describe the transformation applied to the graph of p(x) = 2* that forms the new function q(x) = 2*-3 + 4. %3!

Describe the transformation applied to the graph of p(x) = 2* that forms the new function q(x) = 2*-3 + 4. %3!

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.4: Operations On Functions
Problem 124E
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Question
### Problem 14: Describe the transformation applied to the graph of \( p(x) = 2^x \) that forms the new function \( q(x) = 2^{x-3} + 4 \). ### Solution: To describe the transformation from \( p(x) = 2^x \) to \( q(x) = 2^{x-3} + 4 \): 1. **Horizontal Shift**: The term \( (x-3) \) inside the exponent indicates a horizontal shift. Specifically, \( p(x) = 2^x \) shifts to the right by 3 units to form \( 2^{x-3} \). 2. **Vertical Shift**: The additional \( +4 \) outside of the exponential function indicates a vertical shift. The graph of \( 2^{x-3} \) is shifted upwards by 4 units to form \( q(x) = 2^{x-3} + 4 \). Thus, the graph of \( p(x) = 2^x \) is first shifted to the right by 3 units and then shifted upwards by 4 units to form \( q(x) = 2^{x-3} + 4 \).
Transcribed Image Text:### Problem 14: Describe the transformation applied to the graph of \( p(x) = 2^x \) that forms the new function \( q(x) = 2^{x-3} + 4 \). ### Solution: To describe the transformation from \( p(x) = 2^x \) to \( q(x) = 2^{x-3} + 4 \): 1. **Horizontal Shift**: The term \( (x-3) \) inside the exponent indicates a horizontal shift. Specifically, \( p(x) = 2^x \) shifts to the right by 3 units to form \( 2^{x-3} \). 2. **Vertical Shift**: The additional \( +4 \) outside of the exponential function indicates a vertical shift. The graph of \( 2^{x-3} \) is shifted upwards by 4 units to form \( q(x) = 2^{x-3} + 4 \). Thus, the graph of \( p(x) = 2^x \) is first shifted to the right by 3 units and then shifted upwards by 4 units to form \( q(x) = 2^{x-3} + 4 \).
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