Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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**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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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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