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10 17 16- 15 14 13 12 11 10 4x f(x) = 4 %3D O f(x) = 2* f(x) = 4

10 17 16- 15 14 13 12 11 10 4x f(x) = 4 %3D O f(x) = 2* f(x) = 4

Algebra and Trigonometry (6th Edition)
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,...
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**Transcription and Analysis for Educational Website** --- **Task:** Find the exponential function that represents the graph shown. **Graph Description:** The graph presented is a downward-sloping exponential curve, starting from high positive values on the left and approaching zero as it moves to the right. The x-axis ranges from -5 to 5, and the y-axis ranges from -2 to 18. The red curve demonstrates exponential decay. **Multiple-Choice Options:** 1. \( f(x) = \frac{1}{2} \cdot 4^x \) 2. \( f(x) = 4 \left( \frac{1}{4} \right)^x \) 3. \( f(x) = 2^x \) 4. \( f(x) = 4 \left( \frac{1}{2} \right)^x \) **Explanation of the Graph:** - The graph shows exponential decay, typically characterized by a function where the base of the exponent is between 0 and 1. - The behavior of the graph suggests it matches one of the given functions based on its asymptotic trend towards the x-axis. **Conclusion:** Analyze the functions to determine which one represents the graph accurately. Functions with a base of less than 1 in the exponent will show decay, similar to the red curve in the graph.
Transcribed Image Text:**Transcription and Analysis for Educational Website** --- **Task:** Find the exponential function that represents the graph shown. **Graph Description:** The graph presented is a downward-sloping exponential curve, starting from high positive values on the left and approaching zero as it moves to the right. The x-axis ranges from -5 to 5, and the y-axis ranges from -2 to 18. The red curve demonstrates exponential decay. **Multiple-Choice Options:** 1. \( f(x) = \frac{1}{2} \cdot 4^x \) 2. \( f(x) = 4 \left( \frac{1}{4} \right)^x \) 3. \( f(x) = 2^x \) 4. \( f(x) = 4 \left( \frac{1}{2} \right)^x \) **Explanation of the Graph:** - The graph shows exponential decay, typically characterized by a function where the base of the exponent is between 0 and 1. - The behavior of the graph suggests it matches one of the given functions based on its asymptotic trend towards the x-axis. **Conclusion:** Analyze the functions to determine which one represents the graph accurately. Functions with a base of less than 1 in the exponent will show decay, similar to the red curve in the graph.
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