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,...
Related questions
Question
![**Mathematics Exercise: Transforming Functions**
**Question:**
What is the new function \( g(x) \) after vertically stretching \( f(x) = 5^{(x-2)} \) by a factor of 3?
**Instructions:**
To answer this question, you can use the \(\sqrt{x}\) button below this question ("Insert Math Equation") to enter math symbols and create exponents. You can also use the '^' symbol to indicate exponents.
---
**Answer:**
To vertically stretch a function \( f(x) \) by a factor of 3, you multiply the function by 3. Therefore,
If \( f(x) = 5^{(x-2)} \), then
\[ g(x) = 3 \cdot f(x) = 3 \cdot 5^{(x-2)} \].
So the new function \( g(x) \) is:
\[ g(x) = 3 \cdot 5^{(x-2)} \].
---
**HTML Editor Note:**
For those interested in formatting or editing the mathematical expressions visually, the HTML Editor can be utilized. This tool allows for inserting various math symbols and creating mathematical equations seamlessly.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F45e4ee6c-a715-4803-9fbe-92a41a442b45%2Fa1d4b844-164b-445f-a90d-207ce148a071%2F0it8e19_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Mathematics Exercise: Transforming Functions**
**Question:**
What is the new function \( g(x) \) after vertically stretching \( f(x) = 5^{(x-2)} \) by a factor of 3?
**Instructions:**
To answer this question, you can use the \(\sqrt{x}\) button below this question ("Insert Math Equation") to enter math symbols and create exponents. You can also use the '^' symbol to indicate exponents.
---
**Answer:**
To vertically stretch a function \( f(x) \) by a factor of 3, you multiply the function by 3. Therefore,
If \( f(x) = 5^{(x-2)} \), then
\[ g(x) = 3 \cdot f(x) = 3 \cdot 5^{(x-2)} \].
So the new function \( g(x) \) is:
\[ g(x) = 3 \cdot 5^{(x-2)} \].
---
**HTML Editor Note:**
For those interested in formatting or editing the mathematical expressions visually, the HTML Editor can be utilized. This tool allows for inserting various math symbols and creating mathematical equations seamlessly.
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